Does the time difference between Rome and Vancouver change during the year?

Yes. Because of daylight saving time the gap moves between +8h and +9h.

When is the best time to call Vancouver from Rome?

There is no overlap between standard working days, so one side has to call early or late.

Rome is 9h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.

Rome

Italy

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Vancouver

Canada

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A 9-to-5 working day in Rome does not overlap one in Vancouver at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Rome · Italy	Europe/Rome	UTC+2
Vancouver · Canada	America/Vancouver	UTC−7

What is the time difference between Rome and Vancouver?: Rome is 9h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.
Does the time difference between Rome and Vancouver change during the year?: Yes. Because of daylight saving time the gap moves between +8h and +9h.
When is the best time to call Vancouver from Rome?: There is no overlap between standard working days, so one side has to call early or late.