  We show that it is possible to construct supersymmetric three-generation
models of Standard Model gauge group in the framework of non-simply-connected
elliptically fibered Calabi-Yau, without section but with a bi-section. The
fibrations on a cover Calabi-Yau, where the model has 6 generations of SU(5)
and the bundle is given via the spectral cover description, use a different
description of the elliptic fibre which leads to more than one global section.
We present two examples of a possible cover Calabi-Yau with a free involution:
one is a fibre product of rational elliptic surfaces $dP_9$; another example is
an elliptic fibration over a Hirzebruch surface. There we give the necessary
amount of chiral matter by turning on in the bundles a further parameter,
related to singularities of the fibration and the branching of the spectral
cover.
