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A function $v\\in L^1(I;LD_{div}(B))$ is a solution to the non-stationary $\\mathcal A $-Stokes problem iff \\begin{align}\\label{abs} \\int_Q v\\cdot\\partial_t\\phi\\,dx\\,dt-\\int_Q \\mathcal A(\\varepsilon(v),\\varepsilon(\\phi))\\,dx\\,dt=0\\quad\\forall\\phi\\in C^{\\infty}_{0,div}(Q), \\end{align} where $Q:=I\\times B$, $B\\subset\\mathbb R^d$ bounded. If the l.h.s. is not zero but small we talk about almost solutions. We present an approximation result in the fashion of the $\\mathcal A$-caloric approximation for the non-stationary $\\mathcal A $-Stokes problem. 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