Transitive hyperidentity in semigroups

In this paper we characterize all semigroups in which the hyperidentity of transitivity $X(X(x,y), X(y,z)) = X(x,z)$ is polynomially satisfied. In particular, we show that every transitive semigroup (that is a semigroup with the identity $xy^2z = xz$) is also hypertransitive.