Consider a homomorphism $f$ between two complexes of vector bundles over a fixed smooth manifold $M$. $$ \cdots \to V_{i - 1} \xrightarrow{\delta_{i-1}} V_i \xrightarrow{\delta_i} V_{i + 1} \to \cdots $$ $$ \cdots \to W_{i - 1} \xrightarrow{\Delta_{i-1}} W_i \xrightarrow{\Delta_i} W_{i + 1} \to \cdots $$ When people (e.g. those working in derived algebraic geometry) say that $f$ is a quasi-isomorphism, does that simply mean that we have isomorphisms $\frac{\ker \delta_i}{\operatorname{im} \delta_{i-1}}|_x \to \frac{\ker \Delta_i}{\operatorname{im} \Delta_{i-1}}|_x$ for all $x \in M$?
I'm worried since $\frac{\ker \delta_i}{\operatorname{im} \delta_{i-1}}$ may not form a smooth vector bundle.
