  We present a class of mappings between the fields of the Cremmer-Sherk and
pure BF models in 4D. These mappings are established by two distinct
procedures. First a mapping of their actions is produced iteratively resulting
in an expansion of the fields of one model in terms of progressively higher
derivatives of the other model fields. Secondly an exact mapping is introduced
by mapping their quantum correlation functions. The equivalence of both
procedures is shown by resorting to the invariance under field scale
transformations of the topological action. Related equivalences in 5D and 3D
are discussed. A cohomological argument is presented to provide consistency of
the iterative mapping.
