  We study the realization problem which asks if a given oriented link in an
open 3-manifold can be realized as a fiber of a submersion to the Euclidean
plane. We correct the results obtained before by the author which contains an
error and certain imperfection, and investigate a necessary and sufficient
condition for the realization in the words of well-known invariants. We obtain
the condition expressed by the first homology group with mod 2 coefficient.
