Branched coverings and nonzero degree maps between Seifert manifolds

In this note we give a necessary and sufficient condition for the existence of a fiber preserving branched covering between two closed, orientable Seifert manifolds (for sufficiency we need the additional assumption that the genus of the base orbifold of the target manifold ). Combining this with two theorems of Rong we get a necessary and sufficient condition for the existence of a nonzero degree map between two such manifolds.