We have the Leray's theorem: Let $\pi:E\longrightarrow B$ be a fiber bundle with fiber $F$ over a simply connected base space $B$. Assume that in every dimension $n$, $H^{\ast}(F)$ is of finite rank and free. Then there exist a spectral sequence $\left\{(E_r,d_r)\right\}$ with $$ E_2^{p,q}=H^{p}(B)\otimes H^{q}(F) $$ and a filtration $\left\{D_i\right\}$ on $H^{\ast}(E)$ s.t. $$ E_{\infty}=\bigoplus_{p,q}{E_{\infty}^{p,q}}\simeq GH^{\ast}\left( E \right) $$ i.e there is a filtration $\left\{D_i\cap H^n\right\}$ on $H^{n}:=H^{n}(E)$ s.t. $$ H^n=D_0\cap \underset{E_{\infty}^{0,n}}{\underbrace{H^n\supset D_1}}\cap \underset{E_{\infty}^{1,n-1}}{\underbrace{H^n\supset D_2}}\cap \underset{E_{\infty}^{2,n-2}}{\underbrace{H^n\supset \cdots }} $$ What confuses me is why the quotient $\frac{D_p\cap H^n}{D_{p+1}\cap H^n}=E_{\infty}^{p,n-p} $
Another thing that puzzles me is that when we use Leray's theorem to calculate the cohomology of $\mathbb{C}\mathbb{P}^2$, the stable page $E_{\infty}=E_3$ looks like
When $p\geqslant 5$, the cohomology of $H^{\ast}(\mathbb{C}\mathbb{P}^2)$ are all trivial, I don't know how can we attact with it. The concept of spectral sequence makes me feel a cloud of fog. Do we have any good ways to understand it in geometric topology?
I would be grateful if you could help me！