Birational complexity of log Calabi-Yau 3-folds

We study the birational complexity of log Calabi-Yau $3$-folds. For such a pair $(X,B)$ of index one and coregularity zero, we show that cbir(X,B)∈ \0,2,3\. Further, we prove that $(X,B)$ has a log Calabi-Yau crepant birational model that admits a crepant contraction to (P³⁻ᶜ,H₀++H3-c), where c=cbir(X,B). To prove this, we give a geometric characterization of standard P¹-links.