In an article I'm reading, the author is stating :

$O$ is isomorphic to the complement of a zero section of a line bundle over $X$. We have a long exact sequence of (étale) cohomology associated to the fibration : $$ \cdots \to H^{i-2}_c(X) \to H^{i}_c(X) \to H^{i+1}_c(O) \to H^{i-1}_c(X) \to \cdots $$

Is there a result involving a long exact sequence (of cohomology) and the complement of a zero section of a (line) bundle ?

For now, I'm guessing the first and the last term of the sequence above are the cohomology groups of the line bundle : if $Y \to X$ is the linde bundle, then $$H^i_c(Y) = H^{i-2}_c(X).$$ So hypothetically there should be a long exact sequence like : $$ \cdots \to H^{i}_c(Y) \to H^{i}_c(X) \to H^{i+1}_c(O) \to H^{i+1}_c(Y) \to \cdots $$ but I don't understand why.

Thank you.