  Let $t_{\alpha,\beta}\subset S^2\times S^1$ be an ordinary fiber of a Seifert
fibering of $S^2\times S^1$ with two exceptional fibers of order $\alpha$. We
show that any Seifert manifold with Euler number zero is a branched covering of
$S^2\times S^1$ with branching $t_{\alpha,\beta}$ if $\alpha\geq3$.
  We compute the Seifert invariants of the Abelian covers of $S^2\times S^1$
branched along a $t_{\alpha,\beta}$.
  We also show that $t_{2,1}$, a non-trivial torus knot in $S^2\times S^1$, is
not universal.
