Linking two minimal triangulations of CP2

We present an explicit algorithm for linking two "minimal" triangulations of the complex projective plane. The first one is the 9-vertex simplicial triangulation found by Banchoff and Kuhnel [The math. Intelligencer 5-3 (1983), 11-22]; the second one is the contracted triangulation with eight 4-simplexes, built by the third author [Aequationes Math. 37 (1989), 130-140].