The Mayer-Viertoris exact sequence as a (Zariski) descent spectral sequence.

For certain 'spaces' $U,V$ (they are certain Henselizations of subvarieties) I would like to compute (certain etale) cohomology of $U\cup V$ in terms of the corresponding cohomology of the diagram $U\cap V\stackrel{\to}{\to} U\sqcup V$. Is there an easy way/standard references to do this? I know that one can complete the diagram mentioned to the corresponding (Cech) hypercovering, then write the corresponding descent spectral sequence; then one can show that this spectral sequence actually depends only on the diagram mentioned. Yet do I really need simplicial objects in this simple situation? Is there a more direct way to show that one can obtain the Mayer-Viertoris long exact sequence this way? Any references for this??!!

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