  We search for fast-expanding Hi shells associated with Galactic supernova
remnants (SNRs) in the longitude range l \approx 32\arcdeg to 77\arcdeg using
21-cm line data from the Inner-Galaxy Arecibo L-band Feed Array (I-GALFA) Hi
survey. Among the 39 known Galactic SNRs in this region, we find such Hi shells
in four SNRs: W44, G54.4-0.3, W51C, and CTB 80. All four were previously
identified in low-resolution surveys, and three of those (excluding G54.4-0.3)
were previously studied with the Arecibo telescope. A remarkable new result,
however, is the detection of Hi emission at both very high positive and
negative velocities in W44 from the receding and approaching parts of the Hi
expanding shell, respectively. This is the first detection of both sides of an
expanding shell associated with an SNR in Hi 21-cm emission. The
high-resolution I-GALFA survey data also reveal a prominent expanding Hi shell
with high circular symmetry associated with G54.4-0.3. We explore the physical
characteristics of four SNRs and discuss what differentiates them from other
SNRs in the survey area. We conclude that these four SNRs are likely the
remnants of core-collapse supernovae interacting with a relatively dense (>~1
cm^-3) ambient medium, and we discuss the visibility of SNRs in the Hi 21-cm
line.
