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Usually spectral sequences are defined together with a grading on it, the differential $d_r$ on the page $r$ taking $E_r^{p,q}$ to $E_r^{p-r, q+r-1}$.

This convention on the grading on the differential appears to be the standard one. Why is so ?

Setting $\bar E_r^{p,q} = E_r^{p-q, q}$ the diffential takes $\bar E_r^{p,q}$ to $\bar E_r^{p-1, q+r-1}$ which is easier (in my opinion) to handle both for the degree of the diferential and for question of convergence.

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