  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 Mets\"ahovi radio telescope at 37 GHz, from 4 to 11 April
2017. We observe a spectral steepening from $\alpha = 0.2$ to 0.5 (with
$S_{\nu} \propto \nu^{-\alpha}$) 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).
