The term sakkāya-diṭṭhi is the first of ten fetters that is eradicated when someone recognized the first stage of lokuttara citta. The three fetters below:

1. sakkāya-diṭṭhi
2. vicikicchā
3. sīlabbata-parāmāsa

is required to be comprehended as 3 simultaneous fetters that occurs simultaneously. sakkāya-diṭṭhi can be described using analogy of a dog chasing its own tail.
Ordinary person (puthujjana) will see that the dog and its tail is different. When someone tries to tell him/her that actually the dog and the tail is the same, they will reject it as impossible, hence the vicikicchā is arouse in them. Then he/she, believe that in order to end the dukkha, some actions is required (i.e 'chasing the tail'), and hence sīlabbata-parāmāsa is aroused.

Ordinary person since the unknown beginning of samsara is still operate like the above analogy, which is indispensable for the survival. But in the context to end the dukkha, the proverbial dog is required to stop chasing its own tail. When that is happening (i.e. the dog stops), the three fetters will be discarded simultaneously.

But what is happening in the current world today, many still believe that some actions is required to end the dukkha, which is sīlabbata-parāmāsa, and hence, they will never 'achieve' its 'goal' which is the end of dukkha (nibbāna).

So, in the context of higher stages of enlightenment, again using the above analogy, it is the 'speed' of chasing the tail. It is slower on each stages, and stops completely on an Arahant.