I am reading Seidel's paper on exact Lagrangian submanifolds in $T^*S^n$ and the graded Kronecker quiver, and in Lemma 2 (2) he claims the following fact: if $F_0$ is a cotangent fibre and $F_1$ is $\tau_Z(F_0)$, the Dehn twist along the zero section, then $$HF^\bullet(F_0,F_1)\simeq H^\bullet(S^{n-1};\mathbb{C})$$ (all Lagrangians brane are equipped with the trivial line bundle). He says that one can perturb the Lagrangians so that they intersect cleanly along $S^{n-1}$ and hence, by what he calls standard Bott-Morse methods, the isomorphism follows.
However, I am not quite sure what this means - I have only seen Bott-Morse theory, using the pearl complex, applied in calculating the self-Floer cohomology of a Lagrangian $L$, perhaps with different branes. How is one to apply this in the current scenario with $F_0$ and $F_1$? The only thing that comes to mind is perhaps we can undo the Dehn twist but affect the Lagrangian brane, and then apply the pearl complex, i.e. if we have flat vector bundles $\xi, \xi'$, then perhaps:$$HF^\bullet((F_0, \xi),(\tau_Z(F_0), \xi'))\simeq HF^\bullet((F_0,\xi), (F_0, \tau_Z^*\xi'))\simeq H^\bullet(F_0; \xi \otimes \tau_Z^*\xi')$$
Apologies if this is a bad question - I would appreciate any references to the type of method Seidel is using here.
