Splitting Neutrino masses and Showering into Sky

Neutrino masses might be as light as a few time the atmospheric neutrino mass splitting. The relic cosmic neutrinos may cluster in wide Dark Hot Local Group Halo. High Energy ZeV cosmic neutrinos (in Z-Showering model) might hit relic ones at each mass in different resonance energies in our nearby Universe. This non-degenerated density and energy must split UHE Z-boson secondaries (in Z-Burst model) leading to multi injection of UHECR nucleons within future extreme AUGER energy. Secondaries of Z-Burst as neutral gamma, below a few tens EeV are better surviving local GZK cut-off and they might explain recent Hires BL-Lac UHECR correlations at small angles. A different high energy resonance must lead to Glashow's anti-neutrino showers while hitting electrons in matter. In water and ice it leads to isotropic light explosions. In air, Glashow's anti-neutrino showers lead to collimated and directional air-showers offering a new Neutrino Astronomy. Because of neutrino flavor mixing, astrophysical energetic tau neutrino above tens GeV must arise over atmospheric background. At TeV range is difficult to disentangle tau neutrinos from other atmospheric flavors. At greater energy around PeV, Tau escaping mountains and Earth and decaying in flight are effectively showering in air sky. These Horizontal showering is splitting by geomagnetic field in forked shapes. Such air-showers secondaries release amplified and beamed gamma bursts (like observed TGF), made also by muon and electron pair bundles, with their accompanying rich Cherenkov flashes. Also planet's largest (Saturn, Jupiter) atmosphere limbs offer an ideal screen for UHE GZK and Z-burst tau neutrino, because their largest sizes. Titan thick atmosphere and small radius are optimal for discovering up-going resonant Glashow resonant anti-neutrino electron showers. Detection from Earth of Tau, anti-Tau, anti-electron neutrino induced Air-showers by twin Magic Telescopes on top mountains, or space based detection on balloons and satellites arrays facing the atmosphere's limbs are the simplest and cheapest way toward UHE Neutrino Astronomy Horizons