Crossover rivals

I am thinking of setting the cannon characters to have crossover rivals with others. Some would be in the show as them while others different. They may either be male or female. The rivalry can be not just about love, but also in fights as well.

Ryomou Shimei (Ikkitousen series):

1) Kan'u Unchou (Ikkitousen series)- ideas open on the description on her rivalry with Kan'u
2) Rio Kazama (Wanna Be the Strongest in the World)- ideas open on the description on her rivalry with Rio
3) Ryofu Housen (Ikkitousen series)- ideas open on the description on her rivalry with Ryofu
4) Alphard Alshua (CANAAN)- ideas open on the description on her rivalry with Alphard
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Tier Halibel (Bleach):

1) Erza Scarlet (Fairy Tail)- ideas open on the description on her rivalry with Erza
2) Oda Nobunaga (Battle Girls: Time Paradox)- ideas open on the description on her rivalry with Oda
3) Esdeath (Akame Ga Kill!)- ideas open on the description on her rivalry with Esdeath
4) Alphard Alshua (CANAAN)- ideas open on the description on her rivalry with Alphard
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Tsukiumi (Sekirei):

1) Oda Nobunaga (Battle Girls: Time Paradox)- ideas open on the description on her rivalry with Oda
2) Esdeath (Akame Ga Kill!)- ideas open on the description on her rivalry with Esdeath
3) Ryofu Housen (Ikkitousen series)- ideas open on the description on her rivalry with Ryofu
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Killer Bee (Naruto):

1) Samui (Naruto)- ideas open on the description on his rivalry with Samui
2) Guren (Naruto)- ideas open on the description on his rivalry with Guren
3) Mai (Naruto)- ideas open on the description on his rivalry with Mai
4) Roshi (Naruto)- ideas open on the description on his rivalry with Roshi
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If there any suggestions on any of them, let me know.