I have recently been learning about spectral sequences, not in the context of any problem, but mostly out of curiosity. There are two questions that have occurred to me which I've been unable to answer, even after computing a few examples.

For the purposes of both questions, suppose I have two filtered chain complexes: $0=C_{0}\subset C_{1}\subset\ldots\subset C_{n}$ and $0=K_{0}\subset K_{1}\subset\ldots\subset K_{m}$. For the sake of these questions one can assume that the modules making up the complexes are finite dimensional vector spaces.

If $n=m$ and there exists $q$, such that $0<q<n$, and for all $p\neq q$ $K_{p}=C_{p}$, then what is the relationship between the spectral sequences associated to each filtration? To put it another way, if I change a filtration at one level, how does the associated spectral sequence change?

If $m<n$ and there exist $m$ integers $0\leq i_{0}<i_{1}<\ldots<i_{m} \leq n$ such that $K_{k}=C_{i_{k}}$, then how are the spectral sequences of the two complexes related. That if I forget certain $C_{i}$ to form a new (shorter ) filtration for the same complex, how does the spectral sequence change?