Panels (a)–(b): Cut-out of the time evolution (between 100 and 400 Myr) for the gas inflow (panel a) and outflow (panel b) rate at the vicinity of the MBH (through a spherical shell at R = [1, 3] pc) for different ISM phases (coloured lines), in our Stellar Feedback simulations (see Table 2). Panel (c): Corresponding time evolution of the MBH gas accretion rate and its Eddington accretion limit (solid and dash-dotted black line, respectively). Panel (d): As a function of time, the total gravitational binding- (solid blue line), thermal- (dashed orange line), and kinetic energy (dotted green line) of all the inflowing and outflowing gas between R = [1, 3] pc. Panel (e): Radial distances (with respect to the position of the MBH) to nearby SNII explosions as a function of time.