Let v_d(ℙ²) ϵ |O_ℙ²(d)| denote the d-uple Veronese surface. After studying some general aspects of the wall-crossing phenomena for stability conditions on surfaces, we are able to describe a sequence of flips of the secant varieties of v_d(ℙ²) by embedding the blow-up bl_vd(ℙ²) |O_ℙ²(d)| into a suitable moduli space of Bridgeland semistable objects on ℙ².