In 1982, Leighton proved that any two finite graphs with a common cover admit a finite sheeted common cover. In this talk, I will introduce the combinatorial model $X_{m,n}$ for the Baumslag-Solitar group BS(m,n), and classify for which pairs of integers (m,n) Leighton’s theorem can be extended to the orbit space of covering actions on $X_{m,n}$.