We define blue E/S0 galaxies as objects having a clear early-type morphology on the HST/ACS images but with a blue rest-frame color. We isolate this way 210 IAB < 22 blue early-type galaxies with M* / Msun > 1010 in the COSMOS field located in three redshift bins (0.2 < z < 0.55, 0.55 < z < 0.8, 0.8 < z < 1.4) and study their properties (number density, SFR, morphology, environment, size). The threshold mass (Mt) defined at z=0 in previous studies as the mass below which the population of blue early-type galaxies starts to be abundant relative to passive E/S0s, evolves from log(M* / Msun) ˜ 10.1±0.35 at z˜ 0.3 to log(M* / Msun) ˜ 10.9±0.35 at z ˜ 1. Interestingly it follows the evolution of the crossover mass between the early and late type population (bimodality mass) indicating that the abundance of blue E/S0 is another measure of the downsizing effect in the build-up of the red-sequence. Above log(M* / Msun) ˜ 10.8 blue E/S0 resemble to merger remnants probably migrating to the red-sequence in a short time-scale. Below this mass, they seem to be closer to normal late-type galaxies as if they were the result of minor mergers which triggered the central star-formation or were rebuilding a disk from the surrounding gas in a much longer time-scale. This turn-over mass does not seem to evolve significantly from z˜1 in contrast with the threshold mass and therefore does not seem to be linked with the relative abundance of blue E/S0s.