  We establish several useful commutative diagrams consisting of low term exact
sequences attached to {\Grot} spectral sequences, which extends and integrates
the previous ones appeared in literature such as Alexei~N. Skorobogatov [Beyond
the {M}anin obstruction, Invent. Math. (1999)], and [On the elementary
obstruction to the existence of rational points, Mathematical Notes (2007)].
Parts of the diagrams was frequently used in local-global principle to rational
points.
