I'm not 100% clear what you're trying to say, but if you mean that it is spanning two different time periods (like in history), the correct way to say this is: "Spanning two periods..." No "in" or "during" is needed in this case.

Spans of periods sounds very strange, I don't know what you mean.

Neither is correct, I'm afraid, because 'spans of period' is not a normal phrase. Perhaps 'in two time periods'? If you can tell us the full sentence and context, we'd be in a better position to suggest a suitable phrasing.