The image on the left is Kodaira's table of Singular fibers. It lists all possible fibers in an elliptic fibration over the complex unit disc. 

This report is from a project I did at the Australian National University under Prof. Peter Bouwknegt. 

The picture shows two T-dual manifolds with a given background flux "h". String theories on these manifolds are equivalent, resulting in experiments leading to equivalent observations. Thus, physics can't really distinguish between these topologies.