Consider the class of all languages $L$ that have a randomized algorithm $A$ that runs in worst-case polynomial time such that for any input $x$ if $x \in L$ then $Pr[A(x)\quad \textrm{accepts}] \ge 1/2 - \epsilon_1$; otherwise $Pr[A(x) \quad \textrm{accepts}] \le \epsilon_2$.
Is there any $\epsilon_1 \ge 0$ and $\epsilon_2 > 0$ that make this class equal to BPP? If it is, what are the largest values $\epsilon_1$ and $\epsilon_2$ that we can get (perhaps, relative to each other)?