Equality, yoga would presumably mean that heterosexuals could enter into a civil partnership, which would be a slightly different contract to a marriage. You'd still have to sign on the dotted line though. Otherwise what would there be to prevent someone whose friend had just died suddenly claiming that they were partners and can I have a pension please etc.
I think it is a good idea to have 2 levels. One which is a civil partnership open to all, including brothers and sisters or same sex platonic friends who live together in a long term household. This would cover things like pensions and wills but perhaps could be dissolved under different arrangements than a divorce.
The other a "marriage" which is a promise to forsake all others etc. Harder to dissolve.
But sorting out the difference between the two is not a job I would volunteer for.