This paper provides a concise procedure for the study on local behavior of solutions to anisotropic weighted quasi-linear singular parabolic equations of $p$-Laplacian type, which is realized by applying intrinsic scaling factor to the De Giorgi truncation method. In particular, it also presents a new proof for local H\"{o}lder continuity of the solution in the unweighted case. Finally, the results are further extended to more general doubly nonlinear parabolic equations.
Comment: First, we redefine the intrinsic scaling factors by adding a level parameter to correct the result of Lemma 3.1. Second, Lemma 3.3 is corrected based on an important observation from the energy estimates