abstract: For a family of alpha-continued fraction maps $T\alpha$, we say that $\alpha$ is in the matching set if there are positive integers $M, N$ such that $TzM(z-1) = TzN(z)$ holds for all $z$ in a neighbourhood of $\alpha$. In recent joint work with Carlo Carminati, Niels Langeveld and Hitoshi Nakada, we focus on the map $T\alpha(x) = 1x - 1/x+1-\alpha$ defined by Tanaka and Ito (1981). For alpha-Rosen continued fractions, some matching intervals were given in joint work with Karma Dajani and Cor Kraaikamp (2009).