What is mainly uncovered by Analyzing Causes? Anicca or Dukkha or Anatta?

The suttas with the most references to anicca, dukkha, anatta together are:

AN9.36:0.1: Numbered Discourses 9.36
SN12.66:0.1: Linked Discourses 12.66

AN9.36 teaches us to relinquish the grasping at impermanence:

AN9.36:9.3: So yadeva tattha hoti vedanāgataṁ saññāgataṁ saṅkhāragataṁ viññāṇagataṁ, te dhamme aniccato dukkhato rogato gaṇḍato sallato aghato ābādhato parato palokato suññato anattato samanupassati.
AN9.36:9.3: They contemplate the phenomena there—included in feeling, perception, choices, and consciousness—as impermanent, as suffering, as diseased, as a boil, as a dart, as misery, as an affliction, as alien, as falling apart, as empty, as not-self.
AN9.36:9.4: So tehi dhammehi cittaṁ paṭivāpeti.
AN9.36:9.4: They turn their mind away from those things,

SN12.66 similarly directs us to self-examination and the realization of the futility of craving.

SN12.66:10.1: Ye ca kho keci, bhikkhave, atītamaddhānaṁ samaṇā vā brāhmaṇā vā yaṁ loke piyarūpaṁ sātarūpaṁ taṁ aniccato addakkhuṁ dukkhato addakkhuṁ anattato addakkhuṁ rogato addakkhuṁ bhayato addakkhuṁ,
SN12.66:10.1: There were ascetics and brahmins of the past who saw the things that seem nice and pleasant in the world as impermanent, as suffering, as not-self, as diseased, and as dangerous.
SN12.66:10.2: te taṇhaṁ pajahiṁsu.
SN12.66:10.2: They gave up craving.

One might simply understand the main contribution here as the ignorance of the futility of craving. Specifically, note that in both suttas, the instructions are clear and effective, focusing on the way out of the mess rather than how the mess began. In other words, the main contribution is indirectly implied as a habitual clinging to ignorance.

The dukkha characteristic means it is seen there is no lasting happiness in impermanent things, as explained in SN 22.59. 'Dukkha' here means 'unsatisfactory' rather than 'suffering'. For example, in the meditative attainment of jhana, there is no shifting of postures however dukkha is seen. The suttas say:

Take a mendicant who, quite secluded from sensual pleasures, secluded from unskillful qualities, enters and remains in the first absorption.

Idha, bhikkhave, bhikkhu vivicceva kāmehi …pe… paṭhamaṁ jhānaṁ upasampajja viharati.

They contemplate the phenomena there — included in form, feeling, perception, mental formations and consciousness — as impermanent, as unsatisfactory, as diseased, as a boil, as a dart, as misery, as an affliction, as alien, as falling apart, as empty, as not-self.

So yadeva tattha hoti rūpagataṁ vedanāgataṁ saññāgataṁ saṅkhāragataṁ viññāṇagataṁ, te dhamme aniccato dukkhato rogato gaṇḍato sallato aghato ābādhato parato palokato suññato anattato samanupassati.

AN 9.36

Causality fits into this because it is only conditioned things (things coming to be, remaining & dissolving due to causes) that are impermanent & unsatisfactory. The suttas say:

“Monks, whether Tathāgatas arise or not, this aspect of the world remains the same – this stable truth, this fixed truth: All conditional things are impermanent. A Tathāgata awakens to that and realizes that. Having awakened to it and realized it, he announces it, teaches it, describes it, expresses it, reveals it, explains it, and clarifies it: ‘All conditional things (saṅkhārā) are impermanent.’

“Monks, whether Tathāgatas arise or not, this aspect of the world remains the same – this stable truth, this fixed truth: All conditional things are unsatisfactory. A Tathāgata awakens to that and realizes that. Having awakened to it and realized it, he announces it, teaches it, describes it, expresses it, reveals it, explains it, and clarifies it: ‘All conditional things (saṅkhārā) are unsatisfactory.’

“Monks, whether Tathāgatas arise or not, this aspect of the world remains the same – this stable truth, this fixed truth: All things are impersonal. A Tathāgata awakens to that and realizes that. Having awakened to it and realized it, he announces it, teaches it, describes it, expresses it, reveals it, explains it, and clarifies it: ‘All things (dhammā) are not-self.’”

AN 3.136

When anicca is seen so is dukkha and anatta. From SN 22.59

What do you think, mendicants? Is form permanent or impermanent?”

“Impermanent, sir.”

“But if it’s impermanent, is it suffering or happiness?”

“Suffering, sir.”

“But if it’s impermanent, suffering, and perishable, is it fit to be regarded thus: ‘This is mine, I am this, this is my self’?”

“No, sir.”

,,,

“So you should truly see any kind of form at all—past, future, or present; internal or external; coarse or fine; inferior or superior; far or near: all form—with right understanding: ‘This is not mine, I am not this, this is not my self.’

And so on for each of the aggregates.