  Ballistic annihilation is an interacting system in which particles placed
throughout the real line move at preassigned velocities and annihilate upon
colliding. The longstanding conjecture that in the symmetric three-velocity
setting there exists a phase transition for the survival of middle-velocity
particles was recently resolved by Haslegrave, Sidoravicius, and Tournier. We
develop a framework based on a mass transport principle to analyze
three-velocity ballistic annihilation with asymmetric velocities assigned
according to an asymmetric probability measure. We show the existence of a
phase transition in all cases by deriving universal bounds. In particular, all
middle-speed particles perish almost surely if their initial density is less
than 1/5, regardless of the velocities, relative densities, and spacing of
initial particles. We additionally prove the continuity of several fundamental
statistics as the probability measure is varied.
