  In the final paper of the Graph Minors series N. Robertson and P. Seymour
proved that graphs are well-quasi-ordered under the immersion ordering. A
direct implication of this theorem is that each class of graphs that is closed
under taking immersions can be fully characterized by forbidding a finite set
of graphs (immersion obstruction set). However, as the proof of the
well-quasi-ordering theorem is non-constructive, there is no generic procedure
for computing such a set. Moreover, it remains an open issue to identify for
which immersion-closed graph classes the computation of those sets can become
effective. By adapting the tools that were introduced by I. Adler, M. Grohe and
S. Kreutzer, for the effective computation of minor obstruction sets, we expand
the horizon of computability to immersion obstruction sets. In particular, our
results propagate the computability of immersion obstruction sets of
immersion-closed graph classes to immersion obstruction sets of finite unions
of immersion closed graph classes.
