There exists a five component link U subset of S-2 X S-1 such that eve
ry closed, connected, orientable 3-manifold M with H-1 (M) not equal 0
is a branched covering over S-2 X S-1 With branching set exactly the
link U. There exists a five component link U subset of S-2 x S-1 such
that every closed, connected, non-orientable 3-manifold M with the Boc
kstein of the first Stiefel-Whitney class, beta omega(1)(M) = 0, is a
branched covering over S-2 x S-1 branched along the link U.