  Let X/G be a 3-dimensional Calabi-Yau orbifold with codimension 2
singularities. The topology of crepant resolutions of X/G is described by the
McKay correspondence (Reid, Ito). We study Calabi-Yau 3-folds Y that arise by
deforming the complex structure of X/G. The McKay correspondence does not hold
for such Y. We describe the topology of Y using the `Weyl group' of the
singular set of X/G. Even in simple examples, this can give many different ways
to desingularize X/G. It would be interesting to interpret these results in
String Theory, which should lead to a generalization of the idea of orbifold
CFT, similar to the idea of `discrete torsion' (Vafa, Witten).
