Your title says on the move, does that mean you don't want to stop and boil the water? If so, you are going to have to look at a chemical treatment after filtration. Iodine or puritabs will do the job, but be aware that if you are pregnant or have a thyroid problem, iodine should be avoided. They will both flavour the water too, and not in a nice way!
Boiling is the best way, I have boiled water and never used puritabs or iodine personally, although I have had a sip of puritabbed water, never again! If you don't mind drinking swimming pool water you'll be just fine!
Also, when you collect water for drinking, apart from checking for dead animals upstream and folk weeing in the stream, try and collect the water from where it flows over a stone or similar. When the water is churned up and frothy white, the sediment is dropped out and this is where you will get the cleanest water, so less work for your filtration system. I have drank water from a stream in UK untreated like this, but if you are not sure, boil it!