Eyes contain the chakra of the original user
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When Sasuke felt Itachi's power flowing in him it was actually his chakra mixing with the chakra in Itachi's eyes
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The EMS pattern basically represents the union of both chakras like Naruto's eyes when he mixes NE with bijuu chakra
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The reason EMS has only worked twice in the entire clan's history is because only siblings of equal eye power have the chakra required to unlock EMS similar to how only Ashura has the chakra required to unlock Rinnegan. Izuna was considered Madara's equal and Itachi was above Sasuke until he became sick.