The Mazur manifold is known as the first example of a cork, that is, a contractible 4-manifold that can change differential structures of 4-manifolds by cut and reglue with a twisting map. The Mazur link is a two-component link that describes the Mazur manifold. Akbulut-Yasui generalized them and constructed a sequence of corks. We name their links Akbulut-Yasui links and make a complete list of exceptional, i.e., non-hyperbolic integral Dehn surgeries along them. We use Martelli-Petronio-Roukema's theorem on exceptional Dehn surgeries along the minimally twisted four chain link.