  We study the role of driving in a two-level system evolving under the
presence of a structured environment. We find that adding a periodical
modulation to the two-level system can greatly enhance the survival of the
geometric phase for many time periods. We show that this effect is mainly
important for a markovian regimen but can still be found when the environment
exhibits non-markovian behavior as time revivals. This knowledge can aid the
search for physical set-ups that best retain quantum properties under
dissipative dynamics.
