  Substructures in protoplanetary disks can act as dust traps that shape the
radial distribution of pebbles. By blocking the passage of pebbles, the
presence of gaps in disks may have a profound effect on pebble delivery into
the inner disk, crucial for the formation of inner planets via pebble
accretion. This process can also affect the delivery of volatiles (such as
H$_2$O) and their abundance within the water snow line region (within a few
au). In this study, we aim to understand what effect the presence of gaps in
the outer gas disk may have on water vapor enrichment in the inner disk.
Building on previous work, we employ a volatile-inclusive multi-Myr disk
evolution model that considers an evolving ice-bearing drifting dust
population, sensitive to dust-traps, which loses its icy content to sublimation
upon reaching the snow line. We find that vapor abundance in the inner disk is
strongly affected by fragmentation velocity (v$_{\rm f}$) and turbulence, which
control how intense vapor enrichment from pebble delivery is, if present, and
how long it may last. Generally, for disks with low to moderate turbulence
($\alpha$ $\le$ 1 $\times$ 10$^{-3}$) and for a range of v$_{\rm f}$, radial
location, and gap depth (especially that of the innermost gaps), can
significantly alter enrichment. Shallow inner gaps may continuously leak
material from beyond it, despite the presence of additional deep outer gaps. We
finally find that the for realistic v$_{\rm f}$ ($\le$ 10 m s$^{-1}$), presence
of gaps is more important than planetesimal formation beyond the snow line in
regulating pebble and volatile delivery into the inner disk.
