>>928553Absolutely. No problem. I don't think you need or want a filter in place. I turn my cultures with airstones to keep them from settling at the bottom of my jugs.
(You can culture much of this stuff in less than a cup of water.)
Getting a little more serious- You just need bottles of PH up and PH down, testing strips, F2 algae food and salt like "instant ocean." Bleach and ethanol hand sanitizer if working with more than 1 culture. For diatoms, you may want a silica supplement. For symbionts, you may want to supplement with something like a couple garden peas. For saline solutions, there's a simple optic tool that will tell you the exact salinity.
Spirulina is really easy and so is chlorella/// I rate them really good beginner algae, and they just happen to be popular nutrient supplements as well which is great.