Regularity of the half-line for Levy processes

Consider a real-valued Levy process X started at 0. One says that 0 is regular for (0, infinity) if X enters (0, infinity) immediately. ROGOZIN proved that 0 is regular for (0, infinity) if X has unbounded variation, and SHTATLAND that if X has bounded variation and drift coefficient delta, then 0 is regular for (0, infinity) when delta > 0 but not when delta < 0. We characterize in terms of their Levy measures the Levy processes with bounded variation and zero drift for which 0 is regular for (0, infinity). The result is related to a Theorem of ERICKSON On the asymptotic behaviour of random walks.