Siebe said, I do not think the sutta’s instruct that one must first use anicca and then dukka and then anatta.
I also don’t think that one needs to first see one and then the others. It is said that if a person sees one of them he sees the other two.
However, it is very clearly mentioned that anicca, dukka and anatta are related. For example in SN22.15 “Yadaniccaṃ taṃ dukkhaṃ; yaṃ dukkhaṃ tadanattā”, which I take to mean if something is anicca it is dukka, if something is duka then it is anatta. The relationship between the anicca, dukka, anatta is clearly mentioned.
This has been translated as “What is impermanent is suffering. What is suffering is non-self.” If we simply go by this translation we can see that this doesn’t make any sense; just because something is impermanent it will not be suffering.
The next phrase in the sutta is “yadanattā taṃ ‘netaṃ mama, nesohamasmi, na meso attā’ti evametaṃ yathābhūtaṃ sammappaññāya daṭṭhabbaṃ”. This has been translated as “What is non-self should be seen as it really is with correct wisdom thus: ‘This is not mine, this I am not, this is not my self.’” Again, this translation is a bit confusing for me. If I understand that something is non-self (not me), then after I understand that it is non-self, I again need to understand that “it is not my-self”.
So from these sutta’s and their translations it is clear to me that anicca does not mean impermanence and anatta does not mean non-self.