On 22nd of September 2017 the IceCube collaboration sent an alert for an EHE (Extreme High Energy) event, corresponding to the reconstruction of a muonic neutrino (IC-170922A) with energy $\sim290$ TeV. A multi-wavelength follow-up campaign associated this neutrino event with a gamma-ray flaring state of the BL Lac TXS 0506+056 located at z=0.3365... From the same position of the sky a muonic neutrino excess is observed in a time window of 110 days around 13th of December 2014. These observations together suggest TXS 0506+056 as a possible neutrino emitter. We report here a short and long term gamma-ray monitoring of this source and we compare it with other blazars selected following the criteria of being spatially correlated with an astrophysical muonic neutrino event observed by IceCube. A detailed study of source duty cycles, as well as the characterization of most significant flares is obtained through the Fermi-LAT data. We show the expected neutrino flux variability with different time binning assuming the gamma-rays observed by Fermi-LAT produced through pion cascades. These expectations are then compared with the IceCube discovery flux level searching for the optimal time bin in a multi-messenger context. (read more)