In p. 58 of Hatcher's book we can find a couple of covering spaces of $S^1\vee S^1$ with its corresponding subgroups.
Given a subgroup $H$ of $\pi_1(S^1\vee S^1)$ (take for example $H=\langle a,b^2,bab^{-1}\rangle$) I am trying to get its corresponding covering space. For do so, I consider $X_H$ to be the quotient space of the universal cover $\tilde X$ of $X$ via the equivalence relation $\sim$ which is given in the proof of the Proposition 1.36.
Unfortunately, I am not able to figure how is $X_H$ with this technique. Is there another way to compute $X_H$?