Filtering When Record Open/Closed Dates Intersect With A Slicer Date Range

Thank you for providing the sample data.

You already mentioned the magic word - INTERSECT.  However in your case you want a filter for Overlap, not just for Intersect.  That means you have to do that in separate steps.

- First identify if your item dates INTERSECT with the slicer date range.  Use FILTERS(Calendar[Date])  as the left table, and use CALENDAR(Deliveries[Delivery Start Date],Deliveries[Delivery End Date]) as the right table.  Note :  you need to do that for each row in the selected table visual

- Then set the flag for each of these rows to yes (intersects) or no (doesn't intersect) and use that flag as a visual or page filter.

My implementation goes a step further and looks at the problem from the perspective of the Grand total.

Count = 
var d = SUMMARIZE(Deliveries,Deliveries[Delivery ID],"Show",IF(COUNTROWS(INTERSECT(FILTERS('Calendar'[Date]),CALENDAR(min(Deliveries[Delivery Start Date]),max(Deliveries[Delivery End Date]))))>0,1,0))
return sumx(d,[Show])

PBIX attached