  We study the heterodimensional dynamics in a simple map on a
three-dimensional torus. This map consists of a two-dimensional driving Anosov
map and a one-dimensional driven M\"obius map, and demonstrates the collision
of a chaotic attractor with a chaotic repeller if parameters are varied. We
explore this collision by following tangent bifurcations of the periodic
orbits, and establish a regime where periodic orbits with different numbers of
unstable directions coexist in a chaotic set. For this situation, we construct
a heterodimensional cycle connecting these periodic orbits. Furthermore, we
discuss properties of the rotation number and of the nontrivial Lyapunov
exponent at the collision and in the heterodimensional regime.
