There is a comparison theorem for spectral sequnces in Weibel's book (5.2.12) stating;

Assume $E_{p,q}$ and $\bar E_{p,q}$ converge to $H_* $ $\bar H_*$ respectively. Furthermore we have given a map $h: H_{*} \to \bar H_{*} $ compatible with a morphism $f$ of spectral sequences.

If $f^r: E^r_{p,q} \to \bar E^r_{p,q}$ is an isomorphism for all $p,q$ and some $r$ then $h$ is an isomorphism.

What I want to ask is what happens if we have a milder situation than isomorphism. For example if they just differ on the border?

To be precise let $E^2_{p,q}$ and $\bar E^2_{p,q}$ are two first quadrant spectral sequences converging to $H_* $ $\bar H_*$ respectively. Also there is a map $h$ compatible with a morphism $f$ of spectral sequences as above. Assume $E^2_{p,q} \cong \bar E^2_{p,q}$ if $q\neq0$ and $E^2_{p,0}$ vanishes. Can we calculate kernel and cokernel of $h$?

Thanks for your help.