Given a filtration $F$ on a chain complex $C$, define two new filtrations $\tilde{F}$ and $Dec(F)$ on $C$ by $\tilde{F}_pC_n=F_{p-n}C_n$ and $(Dec F)_pC_n=\{x\in F_{p+n}C_n\colon d(x)\in F_{p+n-1}C_{n-1}\}$. Show the the spectral sequences for these three filtrations are isomorphic after reindexing: $E_{pq}^r(F)\cong E_{p+n,q-n}^{r+1}(\tilde{F})$ for $r\geq 0$ and $E_{pq}^r(F)\cong E_{p-n,q+n}^{r-1}(Dec F)$ for $r\geq 2$.
My attempt
For the first of these, my thought is to try and prove that the 0th page of the $F$ spectral sequence is isomorphic to the first page of the $\tilde{F}$ spectral sequence. Then using the Mapping Lemma, I could get an isomorphism for all higher pages. As I did not see an immediate way to do this, I tried drawing out the picture of what is going on. Doing so I found that the 0th page of the $F$ spectral sequence gives the same diagram as the $1$st page of the $\tilde{F}$ spectral sequence. However, I don't see how to define a map from one to the other. I know that the shifting of the indices results in the (p,q) lining up between the two spectral sequences. However, I don't see how to get a map going between them. The only idea I have is to use some type of map that sends an element to its corresponding element in the homology. However, I don't believe such a map can even be defined, since the homology only deals with cycles, and not the whole complex.
For the second problem I noticed, using Weibel's notation that $(Dec F)_pC_n=A_{p+n,-p}^1$. I tried to go through using this equality to get some type of relationship between the spectral sequence for the $F$ filtration and that for the $Dec F$ filtration. However, I still do not see what is going on very well. I also tried looking at Deligne's paper where he first defined this filtration. However, I cannot follow much of what he is doing in that paper partially do to him defining spectral sequences for a filtration in a somewhat different of a way than Weibel does.
My understand of spectral sequences as a whole is still fairly poor. I am trying to learn the topic, but find that it is not making much sense to me in how to define maps from one spectral sequence to another.