Abstract
Abstract Let $X$ be a smooth complex projective threefold. We show that if $X_{i}\dashrightarrow X_{i+1}$ is a flip which appears in the $K_{X}$-MMP, then $c_{1}(X_{i})^{3}-c_{1}(X_{i+1})^{3}$ is bounded by a constant depending only on $b_{2}(X)$.
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