It turns out that the different neutrinos are all different states of what is essentially the same particle (kinda like how the different polarizations of a photon are different states of the same particle). Basically, you suddenly see the appropriate particle produced or destroyed. Especially since they didn’t have any differing characteristics between the different neutrino’s. You can then set up another lab miles away (and generally deep underground) to detect the neutrinos produced (for example, the Super-K). In physics we’ve got all kinds of conserved quantities: energy, momentum, baryon number, lepton flavor, color, etc.