Why is the set of k-forms $\Omega^{k}(\varnothing)=0$?

Question

I'm studying cohomology theory from Loring W. Tu- An introduction to Manifolds. And in the construction of the Mayer-Vietoris Sequence, we take a manifold $M$ and an open cover $\left\{U,V\right\}$ of $M$. So in the Mayer-Vietoris Sequence, appears the cohomology group associated to the vector space $\Omega^{k}(U\cap V)$ of the differential forms of degree $k$ on the manifold $U\cap V$. BUT, if $U\cap V=\varnothing$ then is a convention that $\Omega^{k}(U\cap V)=0$. Why this convention works?. Why if we adot this convention we will find the right results and conclusions in calculating the cohomology groups of a manifold?. Depending on the definition we are using, the empty set is not a manifold, so the set of k-forms on it does not make any sense. Please, someone can clarify this for me? Thanks!