  The Anosov-Katok method is one of the most powerful tools of constructing
smooth volume-preserving diffeomorphisms of entropy zero with prescribed
ergodic or topological properties. To measure the complexity of systems with
entropy zero, invariants like slow entropy have been introduced. In this
article we develop several mechanisms facilitating computation of topological
and measure-theoretic slow entropy of Anosov-Katok diffeomorphisms.
