Branched coverings of Seifert fibered solid tori

In a paper published twelve years ago, the author gave a criterion to determine whether there is a fiber preserving branched covering between two given Seifert manifolds, which relies on the special case when the manifolds considered are Seifert fibered solid tori. Here we give an explicit construction of branched covering of a Seifert fibered solid torus by another when their Seifert invariants satisfy certain relation.