Stringy Euler number decreases under three-dimensional flips

Let $f:X\dasharrow Y$ be a flip of two projective $3$-dimensional varieties with log-terminal singularities. Write $e_{\rm st}(X)$ and $e_{\rm st}(Y)$ for their stringy Euler numbers.

Stringy flip conjecture. One has

$$e_{\rm st}(X)>e_{\rm st}(Y).$$

The inequality is known in the toric case when $f$ is a toric flip. The general assertion for projective three-dimensional varieties with log-terminal singularities remains open in the supplied text.