  The present paper is devoted to a study of orientation-preserving
homeomorphisms on three-dimensional manifolds with a non-wandering set
consisting of a finite number of surface attractors and repellers. The main
results of the paper relate to a class of homeomorphisms for which the
restriction of the map to a connected component of the non-wandering set is
topologically conjugate to an orientation-preserving pseudo-Anosov
homeomorphism. The ambient $\Omega$-conjugacy of a homeomorphism from the class
with a locally direct product of a pseudo-Anosov homeomorphism and a rough
transformation of the circle is proved. In addition, we prove that the
centralizer of a pseudo-Anosov homeomorphisms consists of only pseudo-Anosov
and periodic maps.
