effect of possible non-perturbative potentials and flux. Hence our results constitute a good approximation at large moduli values where effects of a non-trivial moduli (super)-potential can be neglected. Particular consideration is given to the evolution of the blow-up moduli; particularly as to whether they may contract, thereby approaching one of the phenomenologically interesting singular limits.

Let us summarise our main results. Starting from the given Kähler potential and consistently truncating off the axions in the chiral moduli multiplets, we show that, after a suitable reparametrisation of fields, the sigma-model metric becomes independent of the blow-up moduli. As a result, these fields can be integrated out and the problem reduces to one of studying the evolution of the bulk moduli in an effective potential. Based on this approach, we show that a number of explicit analytic solutions can be obtained using methods from Toda theory. For all these solutions, we find the relative volume of the blow-up moduli increases asymptotically at early and late times. As a consequence, the small blow-up approximation underlying the Kähler potential breaks down after a finite proper time. This feature can also be intuitively understood from the properties of the effective bulk-moduli potential and can, therefore, 