There are many interesting phenomena in the case of positive or mixed characteristics that defy the geometric intuition obtained from classical complex geometry. For instance, there exist covers of curves whose number of branch points are different but lie in the same flat family. In this talk, we briefly discuss the process of showing that a smooth equal-characteristic p deformation of a cyclic sub-covering extends to that of the whole tower. The result indicates that the p-fibers of the canonical maps between the moduli space of cyclic coverings and one of the sub-coverings are surjective at any closure. The crucial technique is a study of local covering’s degeneration using Kato-Saito-Abbes’ refined Swan conductor, which generalizes the classical perfect residue case.