We discuss a class of linear parabolic equations in non-divergence form in which the leading coefficients are measurable, and they can be singular or degenerate through a weight belonging to a class of Muckenhoupt weights. Krylov-Safonov Harnack inequality for solutions is proved under some smallness assumption on a weighted mean oscillation of the weight. To prove the results, we introduce a class of weighted parabolic cylinders, through which several growth lemmas are established. Additionally, a perturbation method is used and the parabolic Aleksandrov-Bakelman-Pucci type maximum principle is applied to suitable barrier functions. As corollaries, Holder regularity estimates of solutions with respect to a quasi-distance, and a Liouville type theorem are obtained in the paper. The talk is based on the paper arXiv:2409.09437, which is the joint work with S. Cho (Gwangju National University of Education) and my graduate student J. Fang.