Multiple phase spirals suggest multiple origins in Gaia DR3

{\it Gaia} Data Release 2 (DR2) revealed that the Milky Way contains significant indications of departures from equilibrium in the form of asymmetric features in the phase space density of stars in the Solar neighborhood. One such feature is the $z$--$v_z$ phase spiral, interpreted as the response of the disk to the influence of a perturbation perpendicular to the disk plane, which could be external (e.g., a satellite) or internal (e.g., the bar or spiral arms). In this work we use {\it Gaia} DR3 to dissect the phase spiral by dividing the local data set into groups with similar azimuthal actions, $J_\phi$, and conjugate angles, $\theta_\phi$, which selects stars on similar orbits and at similar orbital phases, thus having experienced similar perturbations in the past. These divisions allow us to explore areas of the Galactic disk larger than the surveyed region. The separation improves the clarity of the $z$--$v_z$ phase spiral and exposes changes to its morphology across the different action-angle groups. In particular, we discover a transition to two armed `breathing spirals' in the inner Milky Way. We conclude that the local data contains signatures of not one, but multiple perturbations with the prospect to use their distinct properties to infer the properties of the interactions that caused them.