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Nuclear reactions heat and cool the crust of accreting neutron stars and need to be understood to interpret observations of X-ray bursts and long-term cooling in transiently accreting systems. It was recently suggested that previously ignored neutron transfer reactions may play a significant role in the nuclear processes. We present results from full nuclear network calculations that now include these reactions and determine their impact on crust composition, crust impurity, heating, and cooling. We find that a large number of neutron transfer reactions indeed occur and impact crust models. In particular, we identify a new type of reaction cycle that brings a pair of nuclei across the nuclear chart into equilibrium via alternating neutron capture and neutron release, interspersed with a neutron transfer. While neutron transfer reactions lead to changes in crust model predictions and need to be considered in future studies, previous conclusions concerning heating, cooling, and compositional evolution are remarkably robust.