The flow of gas into and out of galaxies leaves traces in the circumgalacticmedium which can then be studied using absorption lines towards backgroundquasars. We analyse 27 log(N_HI) > 18.0 HI absorbers at z = 0.2 to 1.4 from theMUSE-ALMA Halos survey with at least one galaxy counterpart within a line ofsight velocity of +/-500 km s^{-1}. We perform 3D kinematic forward modellingof these associated galaxies to examine the flow of dense, neutral gas in thecircumgalactic medium. From the VLT/MUSE, HST broadband imaging and VLT/UVESand Keck/HIRES high-resolution UV quasar spectroscopy observations, we comparethe impact parameters, star-formation rates and stellar masses of theassociated galaxies with the absorber properties. We find marginal evidence fora bimodal distribution in azimuthal angles for strong HI absorbers, similar toprevious studies of the MgII and OVI absorption lines. There is no clearmetallicity dependence on azimuthal angle and we suggest a larger sample ofabsorbers are required to fully test the relationship predicted by cosmologicalhydrodynamical simulations. A case-by-case study of the absorbers reveals thatten per cent of absorbers are consistent with gas accretion, up to 30 per centtrace outflows while the remainder trace gas in the galaxy disk, the intragroupmedium and low-mass galaxies below the MUSE detection limit. Our resultshighlight that the baryon cycle directly affects the dense neutral gas requiredfor star-formation and plays a critical role in galaxy evolution.