We use a novel transformation of the reduced Ostrovsky equation to the
integrable Tzitz\'eica equation and prove global existence of small-norm
solutions in Sobolev space H3(R). This scenario is an alternative to
finite-time wave breaking of large-norm solutions of the reduced Ostrovsky
equation. We also discuss a sharp sufficient condition for the finite-time wave
breaking.Comment: 11 pages; 1 figur