It certainly moves like a train.  i love the line

Trains are men and women

and its repetition throughout.  There is something mysterious and beautiful about this line that I can only experience, but can find no words to describe.  Understand, the intention behind this critique is not to correct grammar, punctuation, spelling, or usage.  It is to walk-through the poem in a more subjective sense in which I provide my understanding as a reader, noting which parts I enjoy, which parts I find confusing and why, criticizing mainly indirectly.  I hope it is helpful.

i.

Trains are men and women
holding hands and books
sleeping into each other like piled dogs

Whispering across voids:
ways to tend each other
ways of being there

Lost to the lonely watcher
under sounds of rail and bump
metal drone and solid wind.

This first section moves me quickly into a world that I can understand.  I see it all, though the lines are short, and this is an excellent sign.  I do not yet know why I am listening, but there is a haunting tone of loneliness that seeps into my stomach, settling down deep, intent on sticking around even after I am finished reading.  I can tell all of this even now, before I have read further, and I move onward.  I feel like the action here takes place in a dream and that the speaker, who is scrawling these thoughts and sketches into a notebook, is the dream's creator, though perhaps he is not the dreamer...

ii.

On the train from Scotland, reading Larkin is a brand of imitation.
Running my eyes over the passing horizons
    like proofreading the moment of his creation
Dipping childish fingers in the greatness of that image:
    men and women tying their lives into knots
    a tangle for the untangling of years

I don't detect an obvious shift in scenery, though I strongly suspect one.  I am curious why Larkin is mentioned other than the fact that the speaker is reading...I love the juxtaposition of horizons and text, highly effective, makes me feel like I'm not reading but surveying a landscape....the untangling of years...hmm...intense.

I'm watching this line by line from somewhere far from eyesight
As far as I know Larkin never took this train
The fields and villages seem emptied.
I'm handling his fire across an ocean of noise,
    playing a very tricky tune with stuck fingers
    parading through the notes like a drunk    
with that invisible steam of persistence: a hopeless insistence of becoming.

Still reading, but his mind is wandering, and mine is too, pleased that Larkin speaks to someone, if not me, so that they can call his writing fire, a matter of taste... then there's that interesting little metaphor about the sticky fingers and their tricky tune.  but the last line sort of punctures the effect of the whole thing and I'm snapped back into my own head, outside of the poem looking in, wondering what happened and what that line is supposed to mean.  Reading it again, I see the meaning, but it still doesn't seem interesting or relevant...and then I realize that it was talking about Larkin all the time and I'm suddenly less interested in the whole thing...however, please understand that this remains subjective...objectively, I see the value in discussing your actions at the time, reading Larkin, talk about Larkin, makes sense.

It’s the way we mimic our parents
Papering their forms around the inside of our minds.
There’s a place in the basement for Dad’s Philly accent,
    and Mom’s resigned sigh
A cardboard box of videos to live up to
Families to grow, and stories to write of our lives.
Trains are boys and girls chasing the heat of the setting sun.

and I'm back with all my attention and this is wonderful and there are no words for this, but I understand again, although, what this all had to do with Larkin...I don't know.

iii.

All aboard the Underground
    cattle car packed tight
    pumping blood through a city heart.

If you’ve ever been afraid of something
    Ride the Underground
where your fears pack tight against you
pulling you toward something on the other side:
    a tunnel, and at its end, a light.

A definitive scene shift and moving on to another train, not looking back once, constant motion down the tracks of memory.  And I am agreeing with this idea of the Underground.  I have felt the same about it in my short experience with it.  Mind the gap and all that other rot, but it's a dismal necessary place, and death is certainly near.

Even in King’s Cross, we’re doing our part
    Ride the Underground
Find the meaning of your place in this city
The track will take you
Pulling you along
    like the stale underground air rushing in before the train
    like the plastic bag tumbling along the rails in its wake.

the plastic bag here is perhaps the most haunting, appropriate image I've encountered in a long time.  I'm totally grooving to this whole stanza.

Up above decisions are made, hands are shaken
and here we are
    boarding the train:
    Piccadilly to Cockfosters and back again
    the comings and goings of worldmakers
and here we are down below.
    Ride the Underground.

YES! GO, MAN! GO!

The day black smoke hung over East London scared and excited me.
    Could it happen again?
The clammy grip of reality taking hold
If anything, it was an excuse for outrage
    an outlet for underground angers and underground sorrows.

From the top
    it’s our infrastructure
From below
    it’s the hatred at the end of the line
Somewhere in the middle
    where the sunlight reaches its rubber white fingers in
It’s the emptiness of lives lost:
    this many fewer on the 9 o’clock rush
    the still pictures on the news where the stocks should be.

That day I girded for the struggle between their world and mine
Luckily it was just fire
    to threaten the Games
    unnerve the world again.
Fire to kiss our girders to concrete Earth again.

the ignorant American in me is saying, dammit, I remember something about this on the news, but I have no idea what event he's referencing.  I love the imagery, but my inability to connect this all with reality is irritating, so i read through quickly.

Trains are men and women
    huddled together on a wet Monday night.
There’s a master and slave in every relationship
The Underground--All Aboard--
    is the city’s hidden phallus
        fucking us all into city life.

that is saying a lot and it's bordering on being trite in the way that so many other Freudian-sounding metaphors are trite, but I am willing to accept it because of the wonderful repetition here of "Trains are men and women".  I have no clue what the master/slave bit is about.

iv.

In Paris trains beware
the words of a fuzzy pink hare
    your hands will be sore
    if they’re caught in the door
and I hear that it’s rude to stare.

at this point I become uneasy, wondering if the poem will go off the rail.  fuzzy pink hare?  I don't remember that at all in the Paris trains...the sing-songy meter is throwing me off a little, but then there comes

The subway musicians lay claim
to a peculiar brand of fame
    they don’t stay long
    they play a quick song
and vanish as quick as they came.

and THAT is fantastic.  I want maybe more detail, I feel like I've barely left your head yet in the entire poem, an outing would be just the thing at this point.  Or maybe I'm just biased because I'm a musician myself...

The Berlin Bahn brought me wheeling back to the place
my grandfather once was
armed and green to the teeth,
he spent his euro-trip hugging the ground
    keeping an ear on the radio--I imagine--
    waiting for the good news.

I like this, it's coming closer to the actual you that is the speaker... The grandfather, I can only assume during the war.  cool.

In photos they were smiling:
one in particular shows him with his unit
poking their heads through the windows of a boxcar, waving.
The details are lost with the faces,
    I make them up sometimes when I need to
    it's taking them home, or someplace further
where I know the track never wanders.

I like the death reference at the end, very clever, but I don't understand the part about "the details are lost with the faces".  The details of the faces?  The details of the events?  maybe clarify.  or did you just mean that you don't know what happened to those men?

One story survived the war and came home to us
that my grandfather slashed the canvas of his cot
commissioned a German to paint on it
    the smiling grace of a waiting bridesmaid.
He sent it to her drying--I can imagine the urgency--
and we have it now, still and straining,
an entire era hardened into the face of our roots.

that is a good story.  though the wording is potentially confusing.  I get out of it that the grandpa commissioned a German to paint the face of a waiting bridesmaid on a piece of canvas, cut from his cot.  Then he sent it to her, hurriedly, presumably because he thought he might die or did die...oh, I guess he couldn't have died, because otherwise you wouldn't be writing this...or had he already had children at this point...oh wait no he wasn't married...well that never stopped anyone...I seem to have escalated my own confusion.  Moving on.

Years later on the Bahn from Friedrichstraße to Schönefeld,
having dodged the fare, I scanned the cityscape for the origin of that portrait
that would spawn a body to carry me there
along the tracks of my life.
In its absence I imagined a disembodied voice
telling me that trains are men and women
forever on foot, always tilting homeward.

good use of time markers to bring us back into the present, or more recent past...you know what I mean.  I enjoy the detail of "having dodged he fare".  I'm not sure if I believe the disembodied voice, but this could also be a reference to the birth of this poem in your own mind...if so that is a really interesting concept that I'm totally digging right now... oh, and I just noticed that I think this was supposed to be marked as section v. and the rest may be off...unless you were trying to indicate that this was also part of the same section with Paris...but it does seem like its own section. 

Rubbish of a god:
    the hard hands that built these trains
        and funeral fires.

Iron wind levels
    the cold steel footing of the mind
        when our trains get wrecked.

The impact smacks of
    a sweet kiss, and hands held tight
        when our trains get wrecked.

On a quiet night
    two raccoons sort through rubbish
        and two trains get wrecked.

Ties and rail vibrate
    that trains are men and women
        stirring the good pot.

this seems very Eliot to me for some reason...there seems to be a healthy respect for mystery here which I definitely appreciate.  I don't really have anything too constructive to say about this section other