  In this paper, we generalize the duality between self-dual and
Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking
extension of these theories. The duality is demonstrated with use of the gauge
embedding procedure, both in free and coupled cases, and with the master action
approach. The physical spectra of both Lorentz-breaking theories are studied.
The massive poles are shown to coincide and to respect the requirements for
unitarity and causality at tree level. The extra massless poles which are
present in the dualized model are shown to be nondynamical.
