  In this article, we study localizations of hearts of cotorsion pairs (U,V)
where U is rigid on an extriangulated category B. The hearts of such cotorsion
pairs are equivalent to the functor categories over the stable category of U.
Inspired by Marsh and Palu, we consider the mutation of U that induces a
cotorsion pair (U',V'). Generally speaking, the hearts of (U,V) and (U',V') are
not equivalent to each other, but we will give a generalized pseudo-Morita
equivalence between certain localizations of their hearts.
