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We prove that a certain eventually homological isomorphism between modulecategories induces a triangle equivalence between their singularity categories,Gorenstein defect categories and the stable categories of Gorenstein projectivemodules. Further, we show that Auslander-Reiten conjecture and Gorensteinsymmetry conjecture can be reduced by eventually homological isomorphisms.Applying the results to arrow removal and vertex removal, we describe theGorenstein projective modules over some non-monomial algebras, and we verifythe Auslander-Reiten conjecture for certain algebras.

Eventually homological isomorphisms and Gorenstein projective modules