Overlapping cohort in time eras in cox analysis

[gc_ut]

HI, I have come across an issue regarding overlapping cohorts two time-dependent eras.

I want to see if a specific time period (Era 1 vs Era 2) has affected patients waiting on a list for heart transplant.

However, the patients in Era 1 overlap into Era 2. I do not want to exclude the patients who overlap into Era 2. 

Is there way that SAS to do a multivariate cox regression analysis that will allow for these overlapping cohorts when looking at the effect of an Era (Era 1 vs Era 2).

[PGStats]

Did an abrupt change occur between Era1 and Era2?

You could censor overlapping patients at the end of Era1.

[gc_ut]

Is there a way that I can conduct the analysis without censoring the overlap. I hope to include the overlapped patients.