  The explicit McKay correspondence, as formulated by Gonzalez-Sprinberg and
Verdier, associates to each exceptional divisor in the minimal resolution of a
rational double point a matrix factorization of the equation of the rational
double point. We study deformations of these matrix factorizations, and show
that they exist over an appropriate "partially resolved" deformation space for
rational double points of types A and D. As a consequence, all simple flops of
lengths 1 and 2 can be described in terms of blowups defined from matrix
factorizations. We also formulate conjectures which would extend these results
to rational double points of type E and simple flops of length greater than 2.
