Central models of algebraic varieties

We discuss the CW-complex, associated with an algebraic variety, the cells of which correspond to central models of the variety. The acyclic property of complex, conjectured by me in 2011 in a form of elementary relations of Sarkisov links, was recently verified by my student Yang He. Moreover, he established that the complex is contractible if it is not empty, equivalently, uniruled.