Equivalence of a vector bundle being trivial on $\mathbb{P}^1$

Question

I am looking for various statements about a vector bundle $E$ of arbitrary rank being trivial on the complex projective line, $\mathbb{P}^1$. In particular, some arguments about cohomology would be nice. For example, we know a bundle $E$ on $\mathbb{P}^1$ is trivial if and only if $H^0(E(-1)) = H^1(E(-1)) = 0$.

What other statements in this same vein are equivalent to the triviality of $E$?