Abstract. The mini-landscape of heterotic string compactifications is a set of hundreds of T^6/Z_{6II} orbifold models with the spectrum of the minimal supersymmetric standard model. Those constructions have an anomalous U(1) gauge symmetry that generates a D-term, which has to be canceled by assigning vevs to scalars fields in order to preserve the N=1 supersymmetry. This process breaks global discrete symmetries, decouples exotic states and reduces the gauge sector to give realistic constructions. The vevs of fields located at the orbifold singularities can parametrize the blow-up of the singularities to a generic smooth Calabi-Yau 3-fold. We will start with a review of the heterotic orbifold compactifications and their blown-up counterparts. The smooth CY are studied by a dimensional reduction of the 10d N=1 supergravity theory coupled to super Yang-Mills with an abelian gauge flux in the internal dimensions. I then present the deformation of a T^6/Z_{6II} compactification with MSSM-like spectrum by vevs. I establish the correspondence between the deformed orbifold and a smooth CY 3-fold by identifying the blow-up modes, matching the massless spectrum and comparing the 4d anomaly cancellation mechanism.