  We consider viscosity solutions to non-homogeneous degenerate and singular
parabolic equations of the $p$-Laplacian type and in non-divergence form. We
provide local H\"older and Lipschitz estimates for the solutions. In the
degenerate case, we prove the H\"older regularity of the gradient. Our study is
based on a combination of the method of alternatives and the improvement of
flatness estimates.
