The microquasar Cygnus X-3 underwent a giant radio flare in April 2017, reaching a maximum flux of $sim 16.5$ Jy at 8.5 GHz. We present results from a long monitoring campaign carried out with Medicina at 8.5, 18.6 and 24.1 GHz, in parallel to the Metsahovi radio telescope at 37 GHz, from 4 to 11 April 2017. We observe a spectral steepening from $alpha = 0.2$ to 0.5 (with $S_{ u} propto u^{-alpha}$) within 6 h around the epoch of the peak maximum of the flare, and rapid changes in the spectral slope in the following days during brief enhanced emission episodes while the general trend of the radio flux density indicated the decay of the giant flare. We further study the radio orbital modulation of Cyg X-3 emission associated with the 2017 giant flare and with six mini-flares observed in 1983, 1985, 1994, 1995, 2002 and 2016. The enhanced emission episodes observed during the decline of the giant flare at 8.5 GHz coincide with the orbital phase $phi sim 0.5$ (orbital inferior conjunction). On the other hand the light curves of the mini-flares observed at $15-22$ GHz peak at $phi sim 0$, except for the 2016 light curve which is shifted of 0.5 w.r.t. the other ones. We attribute the apparent phase shift to the variable location of the emitting region along the bent jet. This might be explained by the different accretion states of the flaring episodes (the 2016 mini-flare occurred in the hypersoft X-ray state).
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