Different boolean degrees polynomially related?
It is known that
$$ d_f = O_\epsilon(d_{f,\epsilon}^6), $$
for all $\epsilon &lt; 1/2$. This is described in many lecture notes, for example these quantum lecture notes by Montanaro (Theorem 3). It is suspected that the best exponent is $2$. It is known that the exact value of $\epsilon$ only affects the constant.

Since $d_{f,\epsilon} \leq d_{0,f,\epsilon},d_{1,f,\epsilon} \leq d_f$, the other measures are also polynomially related.