The best way is iCloud. You'll have everything up to date, but you can do it manually if you want.
If you have an Apple ID, you can log in to iCloud.com and create a presentation (web version), but you'll only get transitions - not animations. Animations are not supported in the web version.
The manual way:
- Create your presentation on your MBP
- Email it to yourself
- Make sure you have Keynote installed on your iPhone or iPad
- Open the email on your iPad or iPhone and tap the attachment
- It should open with Keynote
Note: By not using iCloud, you'll have to keep emailing yourself the latest version.
"Is the Mac OS version of Keynote 100% compatible with the iOS version of Keynote on the iPhone/IPP?"
Yes it is. They work exactly the same, but the interface is optimised for touch.
I would recommend that you use iCloud, just to keep it simple, but your workflow is completely doable the way it is as well