Versal deformations in orbit spaces

Given an orbit space M/Γ and an equivalence relation defined in it by means of the action of a group G, we obtain a miniversal deformation of an orbit through a miniversal deformation in M with regard to a suitable group action of G×Γ. We show some applications to the perturbations of m-tuples of subspaces and (C,A)-invariant subspaces.