  Let $v_d(\mathbb{P}^2)\subset |\mathcal{O}_{\mathbb{P}^2}(d)|$ 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 $v_d(\mathbb{P}^2)$ by
embedding the blow-up
$\mbox{bl}_{v_d(\mathbb{P}^2)}|\mathcal{O}_{\mathbb{P}^2}(d)|$ into a suitable
moduli space of Bridgeland semistable objects on $\mathbb{P}^2$.
