While cold dark matter numerical simulations predict steep, ‘cuspy’ density profiles for dark matter halos, observations favor more shallower ‘cores’. The introduction of baryonic physics alleviates this discrepancy, notably as mass fluctuations due to gas inflows and outflows driven by feedback can affect the dark matter distribution. We present and test with numerical simulations a simple theoretical model for the halo response to episodes of such gas inflows and outflows. The model is both able to account for the behavior of spherical shells within the halo and for the variation of the dark matter density profile between two simulation snapshots in a large number of cases. It thus provides a theoretical framework to understand the transition from dark matter cusps to cores, but could also explain the existence of ultra diffuse galaxies, since episodes of inflows and outflows could both expand the dark matter and the stellar distributions.