  Hearts of cotorsion pairs on extriangulated categories are abelian
categories. On the other hand, hearts of twin cotorsion pairs are not always
abelian. They were shown to be semi-abelian by Liu and Nakaoka. Moreover,
Hassoun and Shah proved that they are quasi-abelian under certain conditions.
In this article, we first show that the heart of any twin cotorsion pair has a
largest exact category structure and is always quasi-abelian. We also provide a
sufficient and necessary condition for the heart of a twin cotorsion pair being
abelian. Then by using the results we have got, we investigate the almost split
sequences in the hearts of twin cotorsion pairs. Finally, as an application, we
show that a Krull-Schmidt, Hom-finite triangulated category has a Serre functor
whenever it has a cluster tilting object.
