Let's say you have 300 mana. Casting a 50 mana spell.
If it fills 24 mana, you gonna have worth out of doing it because:
-My way: Cast early (costing 0 gaining 0) Lose 50 mana 2nd cast, 3rd cast you gain 24 and use 0 (because now manaflow is ready in time for 2nd spell rather than first), now you're at 274 mana (if you cast 2nd spell before the cooldown is up [within 75s of first cast], you can adjust the time you have to cast by using up manaflow band later than the recommended time I gave). Your mana gain happens ~10-15 seconds after getting to lane.
-26 total mana lost
-Other way: Cast first (costing 0 gaining 0), 2nd cast you lose 50 mana now you're at 250 mana. You must wait 75s for another mana gain.
-50 total mana lost
You're only including first cast while in lane, my way is assuming you will cast a 2nd after you get to lane BEFORE the cooldown is up.
I'm trying to understand what your comment said but it makes no sense because if you cast a first spell your mana will be full because of manaflow band (which it wouldn't be based on the way you explained my way), cast another that reduces mana, and cast a 3rd which fills it up. Idk what step you missed there.
Sorry for wall of text, I just get annoyed you didn't seem to understand something that could save you more mana, something I tried last game, and something I calculated in advance because I just sat around reading runes and thinking about each one.