Smith Normal Form for block matrix

are there any known results on the smith normal form for block matrices over the integers? In particular I am interested in matrices of size (kr)x(ks) made of square blocks of size k such that each block has one 1 and one -1 in each row and columns and the rest are zeros. This is for computing the cohomology of a certain chain complex.

• What kind of results? Special properties of the Smith form in that case? Efficient computation? A "block-Smith" variant that works on the matrix ring of $k\times k$ matrices? – Federico Poloni Aug 22 '14 at 10:46
• I would like to prove that this kind of matrix have always the same type of smith normal form: an identity matrix and than only zeros. – user53075 Aug 22 '14 at 11:22