Weighted projective lines are introduced by Geigle-Lenzing which give a geometric treatment to the representation theory of the canonical algebras. The study of weighted projective lines is closely related to canonical algebras, cluster algebras, compact Riemann surfaces, Hall algebras and quantum algebras, singularity theory, GL order, and so on. The equivariantization with respect to various finite group actions is very important in the study of weighted projective lines and their derived categories. In this talk, I will show the equivariant equivalence relations induced by degree-shift actions between weighted projective lines.