We analytically calculate the transverse energy fluxes induced in high-power Airy beams by the Kerr self-focusing and the Airy profile itself, respectively. In experimental condition representative of laser filamentation experiments of high-power, ultrashort laser pulses in air and condensed media, the Kerr lens induces transverse energy fluxes much larger than the Airy "prism" at the main peak. As a consequence, the curved plasma channels in Airy beams are not only a plasma spark on a curved focus, but indeed self-guided filaments, and their curved trajectory appears as a perturbation due to the linear Airy propagation regime.