  Any two knots admit orientation preserving homeomorphic Seifert surfaces, as
can be seen by stabilizing. There is a generalization of a Seifert surface to
the setting of links called a C-complex. In this paper, we ask when two links
will admit orientation preserving homeomorphic C-complexes. In the case of
2-component links, we find that the pairwise linking number provides a complete
obstruction. In the case of links with 3 or more components and zero pairwise
linking number, Milnor's triple linking number provides a complete obstruction.
