  New data from Belle and BaBar Collaborations on azimuthal asymmetries,
measured in e+e- annihilations into pion pairs at Q^2=112 GeV^2, allow to take
the first, direct glance at the transverse momentum dependence of the Collins
functions, in addition to their z dependence. These data, together with
available Semi-Inclusive Deep Inelastic Scattering (SIDIS) data on the Collins
asymmetry, are simultaneously analysed in the framework of the generalised
parton model assuming two alternative Q^2 evolution schemes and exploiting two
different parameterisations for the Collins functions. The corresponding
results for the transversity distributions are presented. Analogous data, newly
released by the BESIII Collaboration, on e+e- annihilations into pion pairs at
the lower Q^2 of 13 GeV^2, offer the possibility to explore the sensitivity of
these azimuthal correlations on transverse momentum dependent evolution
effects.
