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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 > 1). 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.

Branched coverings and nonzero degree maps between Seifert manifolds