@StevieC, I've always bought into the idea that "changing your oil without changing your filter is like having a shower and putting your dirty underwear back on".
As such, I've always changed the filter with every OC.
However, I've come to realize* that there's no problem with leaving the filter on for at least two OCs (presuming it's not so full that it will go into bypass mode).
The rationale is that there is typically 0.5 - 1.0 l of old oil left in the engine, even if you do change the filter. The difference in oil volume between a "wet" (has been in service) and "dry" (engine has been rebuilt and not yet filled) engine is usually way more than what the filter holds.
Let's make up some numbers on a mythical modern engine:
Dry capacity: 6.0 l
Wet capacity w/o filter change: 5.0 l
Wet capacity w/ filter change: 5.25 l
So for a normal OC with a filter change, you're draining 5.25 l and leaving 0.75 l of dirty oil in the engine (87.5% new oil).
For an OC without a filter change, you're draining 5.0 l and leaving 1.0 l of dirty oil in the engine (83.3% new oil).
(You could remove a spin-on filter and let it drain, to increase the % of fresh oil you could add. Harder to do with a cartridge filter, but quite easy with a Mazda5 which has a drain plug on the plastic housing.)
If you were really set on having really clean oil without tearing down the engine, you could run the engine with new oil for a short time, drain the mixed oil, and fill with new. Let's be really OCD and say we change the filter too:
After one OC including filter:
Clean oil 87.5% (7/8)
Dirty oil 12.5% (1/8)
After two OCs including filters:
Dirty oil = 1/8 x 1/8 = 1/64 = approximately 1.7%
Clean oil = 63/64 = approximately 98.3%
(I actually did this once after swapping in a used engine.)
* Realize, I say - still can't bring myself to actually do it.