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The association of two IceCube detections, the IceCube-170922A event and a neutrino flare, with the blazar TXS0506+056, has paved the way for the multimessenger quest for cosmic accelerators. IceCube has observed many other neutrinos but their origin remains unknown. To better understand the reason for the apparent lack of neutrino counterparts we have extended the comprehensive dissection of the sky area performed for the IceCube-170922A event to all the 70 public IceCube high-energy neutrinos that are well reconstructed and off the Galactic plane. Using the multi-frequency data available through the Open Universe platform, we have identified numerous candidate counterparts of IceCube events. We report here the classification of all the gamma-ray blazars found and the results of subsequent statistical tests. In addition, we have checked the 4LAC, 3FHL and 3HSP catalogues for potential counterparts. Following the dissection of all areas associated with IceCube neutrinos, we evaluate the data using a likelihood-ratio test and find a 3.23 sigma (post-trial) excess of HBLs and IBLs with a best-fit of 15 +/- 3.6 signal sources. This result, together with previous findings, consistently points to a growing evidence for a connection between IceCube neutrinos and blazars, the most energetic particle accelerators known in the Universe.