  In this article we study the relation between Arinkin's Poincar\'e sheaf on
the compactified Jacobian over an integral nodal curve and the classical
Poincar\'e bundle on the Jacobian of the normalization. This is applied to
derive a formula for the Fourier-Mukai transform of complexes on the
compactified Jacobian that come from pushforward along the normalization map.
This is achieved via a third intermediate geometry: the parabolic modules
introduced by Bhosle and Cook, which enode encode fiber jumps at the nodes.
