pull
close, do up, pull up
open, pull down, undo
get caught in
The fabric got caught in the zip and tore.

be stuck, get stuck, stick
The zip on my bag has stuck.

break
be open, be undone

closure (AmE), fastener (BrE)

with a zip
a bag with a zip
The jacket fastened with a zip at the front.

Zip is used with these nouns as the object:
backpack, dress