Let (R,m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth(

) = d for

. Also we show that, if dim(R) = d and

is a chain of ideals of R such that

is maximal Cohen-Macaulay for all k, then

for every system of parameters

of R. Also, in the case where dim(R) = 2, we prove that the ideal transform

is minimax balanced big Cohen-Macaulay, for every

(R), and we give some equivalent conditions for this ideal transform being maximal Cohen-Macaulay.