Notation in Dolgachev's CAG

Question

On page 497 (page 509 of the pdf) of Dolgachev's CAG (www.math.lsa.umich.edu/~idolga/CAG.pdf) he uses the notation "$\succ_1$". Can someone explain me what that means?

Answer 1

The definition is on page 341, at the bottom. Basically, if $\pi'':X''\to X$, $\pi':X'\to X$ and $\phi:X''\to X'$ are birational morphisms of nonsingular projective surfaces such that $\pi'\phi=\pi''$ and $\phi$ is isomorphic (over $X'$) to the blow-up of a point $x'\in X'$, then by definition $x''\succ_1x'$ if $x''\in\phi^{-1}(x')$.