Covering maps between Seifert fibered manifolds

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Let $M$ and $\widetilde{M}$ be two Seifert fibered three manifolds. Suppose that there exists a covering projection $p: \widetilde{M} \to M$ preserving the Seifert structure. What is the relation between the Euler numbers $e \left( \widetilde{M} \right)$ and $e(M)$ of the two Seifert manifolds?