Not yet reviewed by Pith; the record is open.

The geometry of the neutral gas in and around galaxies is a key regulator of the escape of ionizing photons. We present the first statistical study aiming at linking the neutral and ionized gas distributions to the Lyman continuum (LyC) escape fraction (fesc(LyC)) in a sample of 22 confirmed LyC leakers and non-leakers at z~0.35 using the Keck Cosmic Web Imager (Keck/KCWI) and the Low Resolution Spectrograph 2 (HET/LRS2). Our integral field unit data enable the detection of neutral and low-ionization gas, as traced by Mg II, and ionized gas, as traced by [O II], extending beyond the stellar continuum for 7 and 10 objects, respectively. All but one object with extended Mg II emission also shows extended [O II] emission; in this case, Mg II emission is always more extended than [O II] by a factor 1.3 on average. Most of the galaxies with extended emission are non or weak LyC leakers (fesc(LyC) < 5%), but we find a large diversity of neutral gas configurations around these weakly LyC-emitting galaxies. Conversely, the strongest leakers (fesc(LyC) > 10%) appear uniformly compact in both Mg II and [O II] with exponential scale lengths <1 kpc. We also find a trend between fesc(LyC) and the spatial offsets of the nebular gas and the stellar continuum emission. Moreover, we find significant anti-correlations between the spatial extent of the neutral gas and the [O III]/[O II] ratio, and H$\beta$ equivalent width, as well as positive correlations with metallicity and UV size, suggesting that galaxies with more compact neutral gas sizes are more highly ionized. The observations suggest that strong LyC emitters do not have extended neutral gas halos and ionizing photons may be emitted in many directions. Combined with high ionization diagnostics, we propose the Mg II, and potentially [O II], spatial compactness are indirect indicators of LyC emitting galaxies at high-redshift.