  The spin-1/2 chain with XY anisotropic coupling in the plane and the XX
isotropic dimerized chain are shown to be equivalent in the bulk. For finite
systems we prove that the equivalence is exact in given parity sectors, after
taking care of the precise boundary conditions. The proof is given
constructively by finding unitary transformations that map the models onto each
other. Moreover, we considerably generalized our mapping and showed that even
in case of fully site dependent couplings the XY chain can be mapped onto an XX
model. This result has potential application in the study of disordered
systems.
