nests

[Tiger the Lion]

Hello Anne, and welcome. Lovely poem. Some notes below.

Nests

Outside the back window, across the alley
the food coop’s blue recycle barrels Did you mean coop? or co-op? I don't know if this is a clever pun or a well-worn colloquialism. It works either way, but I need to know. 
loaded with knocked-down materials
are a regular Home Depot
for the local birds.

Flying and swooping above the rot I think this is the best stanza. Please do not start it with "flying and swooping"
and decay, they were a flurry of life
throughout the dead cold of winter
before the last of dropped freezer truck ice these 2 lines finish the thought nicely, but need a trim. Consider the need for "of", "had", "the", also "freezer-truck" hyphenated sounds better to me out loud. I dunno why!
had finally melted into the asphalt.

Before green began poking through the gray cement not a fan of this line break. Ditching "cracks," might fix it.
cracks, their beaks plucked loose
burlap and twine from the piles,
the warp and weft woven into arborvitaes
across from second story windows.

To warm and feather our homes,
we humans scavenge too, only personal opinion but whenever I read "we humans" I feel the writer is dragging me into their metaphor. I know it's about humans, of course it is. I understand the need to segue but I think you can do it better.
from West Elm to farm field flea markets
for the smoothest bed sheets, the comfiest couch,I would prefer a semi-colon or even an em dash here as your list goes from the to the to a. 
a vintage mirror.

Now that the Flowering Crabapple blossoms
block the alley view, we open windows and peek out
from our cozy creations, smell the spring air
and join the birds chirping
in concert with the tulips breaking ground.Don't like "in concert". The meaning is there but music is too dry. 

Good Luck with this. I'll be back,
Paul