cousin complexes and almost flat rings

Let (r, m) be a d-dimensional noetherian local ring and t be a commutative strict algebra with unit element 1t over r such that mt 6= t. we define almost exact sequences of t-modules and characterize almost flat t-modules. moreover, we define almost (faithfully) flat homomorphisms between r-algebras t and w, where w has similar properties that t has as an r-algebra. by almost (faithfully) flat homomorphisms and almost flat modules, we investigate cousin complexes of t and w-modules. finally, for a finite filtration f = (fi)i≥0 of length less than d of spec(t) such that it admits a t-module x, we show that ie 2 p,q := tort p m, h d−q (ct (f, x))
p⇒ hp+q(tot(t )) and iie 2 p,q := hd−p tort q (m, ct (f, x))
p⇒ hp+q(tot(t )), where m is an any flat t-module and as a result we show that ie 2 p,q and iie 2 p,q are almost zero, when m is almost flat