  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 $\sim 290$ 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 long term gamma-ray monitoring of this
source and we compare it with other blazars spatially correlated with
astrophysical muonic neutrino events observed by IceCube. We characterise the
most significant gamma-ray flares of the blazars in the sample and introduce
the blazar duty cycle as an important parameter to be considered when assessing
a possible neutrino counterpart. For the selected blazars we show the expected
neutrino flux variability with different time binning assuming the gamma-rays
observed by Fermi-LAT as a product of a leptohadronic emission scenario. The
neutrino expectations from the blazar sample are then compared with the IceCube
discovery flux searching for the optimal time bin in a multi-messenger context.
This analysis indicates that the detection of a single flare represents a
challenge for a single cubic kilometer detector, underlining the importance of
increasing the size of current neutrino telescopes and obtaining a good
monitoring of the entire sky through a global neutrino network.

High Energy Astrophysical Phenomena