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Ultra high energy neutrinos UHE neutrino Tau, anti-neutrino Tau,anti-neutrino electron at PeVs, and higher energy may induce tau air-showerswhose detectability is million to billion times amplified by their secondaries.We considered UHE nu_{tau}- N and UHE bar\nu_{e}- e interactions beyondmountains as a source of such horizontal amplified Tau air-showers. We alsoconsider vertical upward UHE nu_{tau}-N interaction on Earth crust leading toUHE Tau airshowers {UPTAUS} or at the horizont edges {HORTAUS} and theirbeaming toward high mountains gamma, X, Cherenkov detectors on mountains. Weshow their detectability. We notice that such rare upward Tau air-shower,UPTAUS and HORTAUS, may hit even nearby airlines, ballons, satellite and flashthem by short diluted gamma-burst at the edge of Gamma Ray Observatory (GRO)detection threshold. We suggest the identification of these events with recentdiscovered (BATSE) Terrestrial Gamma Flashes and we claim their probable UHETau by UHE nu_\tau origin. From these data approximated UHE nu_tau flux andDelta m_{nu_mu \nu_tau} lower bound are derived. Known X-gamma-{TeV} activegalactic and extragalactic sources have been identified in most TGF arrivaldirections. Maximal EGRET activity in galactic Center overlap with maximal TGFflux. The UHECR AGASA an-isotropy at 10^{18} eV shows also possiblecorrelations with TGF events. The unique UHECR triplet in AGASA clustering,pointing toward BL Lac 1ES0806+524, finds, within its error box, acorresponding TGF event, BATSE (Trigger 2444). Finally a partial TGF Galacticsignature, combined with above correlations suggests an astrophysical tauorigin of TGF events.Comment: 14 pages text, 13 Fig., 4 Tabs. Minor reductions to a compact form.  Higher definition figures; 4Table; New Appendix A,B,C; Update Reference

Discovering Ultra–High‐Energy Neutrinos through Horizontal and Upward τ Air Showers: Evidence in Terrestrial Gamma Flashes?