Cohomology of a punctured torus using Mayer Vietoris

Question

I have figured out how to use Mayer Vietoris to find cohomology of $T^2$ here. For a punctured torus, following the hint, let $U$ = $T^2\setminus S^1_1$ and $V$ = $T^2\setminus S^1_2$ such the $S^1_1\cap S^1_2$ is the puncture point. Am I correct in saying $H^0(U)=H^0(V)=H^1(U)=H^1(V) = \mathbb{R}$, $H^2(U)=H^2(V)=0$? Also may I know what $U\cap V$ is diffeomorphic to so as to find $H^0(U\cap V)$ and $H^1(U\cap V)$? $U\cap V = T^2\setminus S_1^1\cup S_2^1$.