Transversity distribution describes the quark transverse polarization inside a transversely polarized nucleon. It is the less known leading-twist piece of the QCD description of the partonic structure of the nucleon. Transversity can be extracted from semi-inclusive deep inelastic scattering (SIDIS) where, however, it couples to a new, unknown fragmentation function, called Collins function. We present the preliminary results of the measurement of the azimuthal asymmetries in the process e^+e^- -> qqbar -> pi pi X, where the two pions are produced in opposite hemispheres. These preliminary results are based on a data sample of about 45 fb^{-1}, collected by the BABAR experiment at a center-of-mass energy of 10.54 GeV, and are compared with the Belle measurements.