The mini-cavity in the streamer to the south-west of the dynamical center of the Galaxy, and the unique, nonthermal radio source Sgr A* appear to be physically connected by a chain of plasma ``blobs'' which may be in transit from the latter to the former. Recent observations at radio and infrared wavelengths have provided clear evidence that the cavity has an opening radius of ~ 1^''~ 0.04 pc and radiates with a power L_cav~ 6* 10^37 ergs s^-1. Here, we model the formation of the cavity as the result of an impact between the streamer gas and the post-bow shock gas collimated by a massive (~ 10^6 M_o) black hole coincident with Sgr A*. Multi-wavelength observations, including those of He I, Br\alpha and Br\gagt;~mma line emission in the inner ~ 0.3 pc region of the Galaxy provide strong evidence for the presence of an ambient Galactic center wind with velocity v_w~ 500-700 km s^-1 and mass loss rate ~ 3-4* 10^-3 M_o yr^-1. We show that the Bondi-Hoyle process responsible for the accretion of ~ 10^22 g s^-1 by Sgr A* also produces a downstream, focused flow with a radius very similar to that of the mini-cavity and a mechanical luminosity about 2.5 larger than L_cav. In addition, the size and density of the blobs appear to be consistent with the gas characteristics in this flow.