Dusty, neutral outflows and inflows are a common feature of nearby star-forming galaxies. We characterize these flows in eight galaxies -- mostly AGN -- selected for their widespread NaI D signatures from the Siding Spring Southern Seyfert Spectroscopic Snapshot Survey (S7). This survey employs deep, wide field-of-view integral field spectroscopy at moderate spectral resolution (R=7000 at NaI D). We significantly expand the sample of sightlines in external galaxies in which the spatially-resolved relationship has been studied between cool, neutral gas properties -- N(NaI), Weq(NaI D) -- and dust -- E(B-V) from both stars and gas. Our sample shows strong, significant correlations of total Weq with E(B-V)_stars and g-i colour within individual galaxies; correlations with E(B-V)_gas are present but weaker. Regressions yield slope variations from galaxy to galaxy and intrinsic scatter ~1 Angstrom. The sample occupies regions in the space of N(NaI) and Weq^abs vs. E(B-V)_gas that are consistent with extrapolations from other studies to higher colour excess [E(B-V)_gas ~ 1]. For perhaps the first time in external galaxies, we detect inverse P Cygni profiles in the NaI D line, presumably due to inflowing gas. Via Doppler shifted NaI D absorption and emission lines, we find ubiquitous flows that differ from stellar rotation by >100 km/s or have |v,abs - v,em| > 100 km/s. Inflows and outflows extend toward the edge of the detected stellar disk/FOV, together subtend 10-40% of the projected disk, and have similar mean N(NaI) and Weq(NaI D). Outflows are consistent with minor-axis or jet-driven flows, while inflows tend toward the projected major axis. The inflows may result from non-axisymmetric potentials, tidal motions, or halo infall.
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