Baryons cycle into galaxies from the intergalactic medium and are converted into stars; a fraction of the baryons are ejected out of galaxies by stellar feedback. Here we present new high-resolution (3.''9; 68 pc) 12CO(2-1) and 12CO(3-2) images that probe these three stages of the baryon cycle in the nearby starburst M82. We combine these new observations with previous 12CO(1-0) and [Fe ii] images to study the physical conditions within the molecular gas. Using a Bayesian analysis and the radiative transfer code RADEX, we model temperatures and densities of molecular hydrogen, as well as column densities of CO. Besides the disk, we concentrate on two regions within the galaxy: an expanding super-bubble and the base of a molecular streamer. Shock diagnostics, kinematics, and optical extinction suggest that the streamer is an inflowing filament, with a mass inflow rate of molecular gas of 3.5 M☉ yr–1. We measure the mass outflow rate of molecular gas of the expanding super-bubble to be 17 M☉ yr–1, five times higher than the inferred inflow rate and 1.3 times the star formation rate of the galaxy. The high mass outflow rate and large star formation rate will deplete the galaxy of molecular gas within eight million years, unless there are additional sources of molecular gas.