 Strict transform of an algebraic subvariety

For a blowup of an algebraic variety $\pi :\tilde{X}\to X$ with centre $Z$, the strict transform of an algebraic subvariety of a subvariety $Y$ not contained in $Z$ is the closure of ${\pi }^{-1}(Y\setminus Z)$. It excludes components supported entirely in the algebraic exceptional divisor.