Escaping points of commuting meromorphic functions with finitely many poles

Let $f$ and $g$ be commuting meromorphic functions with finitely many poles. By studying the behaviour of Fatou components under this relation, we prove that have same Julia set whenever no simply connected fast-escaping wandering domains. combining a recent result Tsantaris', obtain strongest statement (to date) regarding sets functions. In order to highlight difference entire case, show transcendental poles orbits alternate between approaching pole escaping infinity at strikingly fast rates.