Continuous means without interruption.
This means that they have a longer string of time for which they have an ancient relic from each period than any other museum.
For example, they might have an ancient relic from every century (100 years) between now and 10,000 years ago. Another museum might have relics from 12,000-10,000 years ago and 8,000 years ago until now, but nothing from 9,000-8,000 years ago. Therefore, it is not "continuous".
If each dash (-) is a time period for which they have an ancient relic, their collection is this:
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and the other museums are like this:
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