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In Earth's galactic neighborhood, there are more than 30 supergiant stars - such as Betelgeuse and Antares - that one day will explode as core collapse supernovae. One such near-Earth supernova will be a truly exceptional event, delivering a multitude of multimessenger signals, the most energetic one being in the form of neutrinos. I will discuss some of these signals that are most characteristic of a near-Earth event, as they might not be observable for more distant galactic supernovae. One of these is the flux of pre-supernova neutrinos, which is a signature of the advanced stages of nuclear burning of the progenitor star, and should be detectable several hours before the collapse. The other is the gamma ray echo of the neutrino burst, due to the absorption of electron antineutrinos in the hydrogen stellar envelope. If time permits, I will briefly mention gravitational waves signatures of the supernova neutrino burst, and how they fit in the complex multi-messenger picture of a collapsing star.