2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65206We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical $r$-matrices and matched pairs induced by Poisson group actions13 pagesDifferential Geometry53D17; 58H05text