Wikipedia said
The description of most manifolds requires more than one chart (a single chart is adequate for only the simplest manifolds). A specific collection of charts which covers a manifold is called an atlas. An atlas is not unique as all manifolds can be covered multiple ways using different combinations of charts. Two atlases are said to be equivalent if their union is also an atlas.
I think it means: Let $X$ be a topological space and $\Phi_1=\{\phi_\alpha:U_{\alpha}\to\Bbb R^{n_\alpha}\mid\alpha\in A\}$, $\Phi_2=\{\phi_\beta:U_{\beta}\to\Bbb R^{n_\beta}\mid\beta\in B\}$ be two of its(i.e., $X$'s) topological atlas. Then $\Phi_1$ and $\Phi_2$ are equivalent iff $\Phi_1\cup\Phi_2$ is also a topological atlas of $X$.
My question is: if $\Phi_1$ and $\Phi_2$ are atlases of $X$, which means they both can "cover" $X$, then it is definitely true that $\Phi_1\cup\Phi_2$ can "cover" $X$, isn't it? I can't see the meaning of such definition of equivalence. Where did I make the mistake?