  We study an electron-hole pair in a stack of multiple quantum dots in the
presence of an external electric field using the configuration interaction
approach. We find that the bright energy levels can be grouped into families
which are associated with the hole localized in a specific dot of the stack.
The exciton energy levels undergo avoided crossings as function of the external
electric field with different pattern for each family. We show that the
variation of the depths of the dots along the stack can be deduced from the
exciton spectrum. In the strong confinement limit the families are mixed by a
weak electric field due to hole tunneling. This results in a characteristic
multiple avoided crossing of energy levels belonging to different families with
an accompanying modulation of the recombination probabilities and an appearance
of a single particularly bright state. We discuss the modification of the
spectrum when dots are added to the stack.
