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A few basic terms that will aid understanding debate on this and other Buddhist forums.
literally ' again becoming ' often translated badly as 'rebirth ' or very badly as 'reincarnation '.
It means our built in tendency to cling to an identity. It might refer to an after death state..but it happens constantly throughout life.
literally 'heaps ' ..our changing bodies, consciousness, perceptions, cognitions, feelings, which are in constant change and from which we weave our self sense. The illusory sense of of a permanent self.
Our repeated clinging to a self sense is one meaning of punabhava..see above.
the Brahma Viharas are a set of four meditations which aim at increasing Metta ( loving kindness ) Karuna ( compassion ) Mudita ( sympathetic joy ) and Upekkha ( equanimity ) in ourselves.
These are seen as arising together and hang together interdependently..metta for example without upekkha can result in attachment.
Upekkha without metta is likely to result in indifference..and so on.
There is a lot of material on the Brahma Viharas to be found on the internet.