  We extend the results of T. Giordano, I. F. Putnam, C. F. Skau contained in
``$\mathbb Z^d$-odometers and cohomology", Groups Geom. Dyn. 13 (2019), no. 3,
P. 909-938, on characterization of conjugacy, isomorphism, and continuous orbit
equivalence of $\mathbb Z^d$-odometers to dimensions $d>2$. We then apply these
extensions to the case of odometers defined by matrices with integer
coefficients.
