Maybe this question is trivial, but I was not able to find an answer. The question is this: Consider the algebraic K-theory of smooth complex projective varieties (such that the K-theory and the G-theory agree). Does it have the Mayer-Vietoris property for the analytic topology? I know it does for the Zarisky topology. If the answer is negative is it possible to have an example?

Update

In view of the comments I felt the need to elaborate my question. Let $X$ be a smooth projective complex variety. Let $G(X)$ be the $K-$theory space of the category of coherent sheaves over $X$. If $U$ and $V$ are two Zariski open subschemes one has the following homotopy cartesian square:$\require{AMScd}$ \begin{CD} G(U \cup V) @>>> G(U)\\ @VVV @VVV \\ G(V) @>>> G(U \cap V) \end{CD}

Does it remain true if $U$ and $V$ are open subsets in the usual (complex) topology of $X$?

Here an open subset $U$ is seen as a ringed space with structure sheaf $\mathcal{O}_X|_U$.