  We show that Lagrangian measurements in active turbulence bear imprints of
turbulent and anomalous streaky hydrodynamics leading to a self-selection of
persistent trajectories - Levy walks - over diffusive ones. This emergent
dynamical heterogeneity results in a super-diffusive first passage distribution
which could lead to biologically advantageous motility. We then go beyond
single-particle statistics to show that for the pair-dispersion problem as
well, active flows are at odds with inertial turbulence. Our study, we believe,
will readily inform experiments in establishing the extent of universality of
anomalous behaviour across a variety of active flows.
