The gemara implies that if one has a chazaka to damage, such as in the case where people had a chazaka to let blood under the trees of rav yosef even though the blood attracted birds which damaged his dates, the chazaka gives them rights to continue. Although the gemara responds that there is no chazaka for damages, the gemara qualifies this to significant damages such as smoke and a bathroom that have a strong stench. Even for minor damages the gemara says that the chazaka won't work if the nizuk is very sensitive, but assuming he is not hypersensitive, a chazka works for small damages.
Tosafos in the name of the Rivam explains that for a chazka for minor damages: 1. No claim is necessary. The reason why the mazik assumes rights through a chazaka is because we assume that the nizuk is mochel on the damage. 2. A chazaka of 3 years is necessary to to prove that the nizuk was mochel. However, Tosafos disagrees and holds that the chazaka must have a claim that mazik actually purchased rights from the nizuk. But, Tosafos implies that they agree with the Rivam that a chazaka on what you are actually machzik such as in this case where they have a chazaka to blood let under the tree, they don't need to claim that they purchased the rights from r' yosef, they can simply claim that after 3 years he was mochel. But when they are trying to expand their chazaka to something beyond what they were doing until now (such as the gemara on 6a where they were trying to put larger beams after making a chazaka for smaller ones), they need to have a valid claim that they purchased it. It comes out that whether or not the mazik needs a ta'ana (claim of purchase) depends on whether he is trying to expand beyond what he was machzik, but regardless he would need a 3 year chazaka.
The rashash points out that Tosafos 6b quotes the rashbam that all the chazakos that were being spoken about in that sugya do not require 3 years, rather the chazaka is achieved immediately. This seems to contradict our Tosafos. The Rashash explains that when the chazaka has a valid claim of purchase, it works immediately, but if the chazaka doesn't have any claim it would require 3 years to substantiate that the nizuk was mochel. This would fit with the haga'ah in rashi 6a who says that 3 years aren't needed, but there must be a claim of purchase. But the haga'ah in rashi implies that without a claim of purchase, even 3 years wouldn't help. Whereas, Tosafos would hold that either 3 years OR a claim of purchase is sufficient.
See also Rashi 7a that a chazaka of use requires 3 years. See rashi 22a that a chazaka for windows requires 3 years. See rashbam 41a and 50b where he seems to hold that one day is enough, as tosafos quotes from rashbam on 6b. But, rashbam on 57a implies that you need 3 years. This can be reconciled based on the approach of the rashash in tosafos that 3 years is needed when there is no claim, but with a claim of purchase 3 years isn't necessary.
The concept of a chazaka without a claim of purchase would seemingly be working through mechila as tosafos holds. But, the ketzos 155:16 points out that if that were true the nizuk should be able to change his mind and not be mochel from here on in. The ketzos understands that it is based on an understanding of neighbors that they can be machzik on one another and it will be binding for the future.