Hi!
I have only seen the show here and there over the years so this is what I know.
Akshara & Naithik had an arrange marriage. Naksh(son) and Naira(daughter) were their kids.
Naira when she was a teenager ran away from home and reconciled with her parents in her early 20's. Her & Karthik fell in love and got married. Kairav(few years older) and Akshara(named after Naira's mom) are their kids.
When Akshara(Akshu) was a only a few months old, Naira fell off a cliff and died. Karthik met Naira's look-a-like named, Sirat who bonded with the kids. She got married to her former lover who eventually died. During all this she & Karthik fell in love, got married and had a daughter, Arohi. Arohi is only maybe a year or 2 younger than Akshu.
Sirat & Karthik raised the kids acting like Naira & Sirat were the same person till Akshu was 9 or 10years old(the older kids like Kairav, Vansh knew the truth). Before Sirat could tell the truth Akshu accidentally found out from a third party but she managed to assure her that Akshu is loved like her own kid. But finding out that Akshu is not her blood sibling led Arohi to be insecure and possesive as her grandmother Sheila(who had hurt Sirat and had been very selfish all along) added fuel to the fire. Sirat & Goenkas did not want the kids anywhere near Sheila because how she was/is as a person but Arohi not understanding the reasons met her anyway. Sirat died in an accident trying to "save" Akshu for which Arohi still blames her. Sirat made(asked) Akshu promise to take care of Arohi but died before she could ask the same from Arohi for Akshu I think. Karthik also died around the same time.
I suggest watching a week or so episodes right before the leap with Akshu & Arohi as kids to better understand the dynamic and characters because I have seen people incorrectly judge these two based on the leap episodes alone.
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