Instanton bundles on the Segre threefold with Picard number three

We study instanton bundles $E$ on $mathbb{P}^1times mathbb{P}^1 times mathbb{P}^1$. We construct two different monads which are the analog of the monads for instanton bundles on $mathbb P^3$ and on the flag threefold $F(0,1,2)$. We characterize the Gieseker semistable cases and we prove the existence of $mu$-stable instanton bundles generically trivial on the lines for any possible $c_2(E)$. We also study the locus of jumping lines.