  For a finite family of 3-dimensional almost contact metric manifolds with
closed the structure form $\eta$ is described a construction of an almost
contact metric manifold, where the members of the family are building blocks -
cells. Obtained manifold share many properties of cells. One of the more
important are nullity conditions. If cells satisfy nullity conditions - then -
in the case of almost cosymplectic or almost $\alpha$-Kenmotsu manifolds -
"sewed cells" also satisfies nullity condition - but generally with different
constants. It is important that even in the case of the generalized nullity
conditions - "sewed cells" are the manifolds which satisfy such conditions
provided the cells satisfy the generalized nullity conditions.
