  We show that the gradient of solutions to degenerate parabolic equations of
porous medium-type satisfies a reverse H\"older inequality in suitable
intrinsic cylinders. We modify the by-now classical Gehring lemma by
introducing an intrinsic Calder\'on-Zygmund covering argument, and we are able
to prove local higher integrability of the gradient of a proper power of the
solution $u$.
