  We find a series of topological phase transitions in a
half-metal/superconductor heterostructure, by tuning the direction of the
magnetization of the half-metal film. These include transitions between a
topological superconducting phase with a bulk gap and another phase without a
bulk gap but has a ubiquitous local gap. At the same time, the edge states
change from counter-propagating Majorana edge modes to unidirectional Majorana
edge modes. In addition, we find transitions between the second phase and a
nodal phase which turns out to be a two-dimensional Weyl superconductor with
Fermi line edge states. We identify the topological invariants relevant to each
phase and the symmetry that protects the Weyl superconductivity phase.
