What is the relationship between the three intertwined stories of The Fountain?

I think that could be reading too much into it and drawing conclusions that are not there. However, that is not to say that isn't the director's intentions as the whole movie is one big symbolic piece.

The way it plays out to me is that the movie is suppose to represent these 2 lovers intertwined in destiny and almost cursed to play out the same role of loving man and dying woman for eternity, no matter the time period.

I am inclined to agree with OP's theory of the present time and 'space bubble' of the future being connected in reality. The position I take is this:

Izzy writes a novel for which the ending is not written (Tommy awakes from the reading to the blank pages). Despite the ending not being written, she has the idea for the ending planned, as she states 'it starts there....but it [ends up relating to Xibalba]' (paraphrasing, dont know the exact quote). That is, Izzy feeds Tommy lore about her historically-based novel in which Xibalba was a means for rebirth. Using this--and by curing death, as he was so adamant to do--he was able to live long enough into a future where he could pilot the bubble into Xibalba.

This has the following additional speculations:

The seed Tommy put upon Izzys casket at her funeral ended up being the tree that he took with him in the space bubble--a reasonable link between how the tree can be related to Izzy.

Tommy wrote the ending of her novel during the space travel. Evidence: If Tommy already continued Izzy's novel with the Conquistador reaching the Tree of Life and subsequently being consumed by it, (for lack of better description) there is no reason the story should then continue to an unrelated, as-of-yet-unmentioned character of the same likeness to go into space with the tree. Therefore, I propose the theory that Tommy cured death and then took the "tree of Izzy" into space. Knowing his long journey ahead and his physical looks, he finishes writing the story, interjecting the space traveler version of himself in the Conquistador story, allowing a ultimate parallel theme to the movie: Izzy dies...Tomas dies. Izzy the tree dies, Tommy the space traveler dies...

In other words, while any version of Tommy can defeat death (immortalization via the tree of life or immortalization by curing death), its the heart--the dedication and passion--and loyalty to her that is paramount.

It's all about the desire of man to stop death. It's all symbolic and very easy to understand. Defeat death by force/science/spirituality. The spain story is about force. Forcing the tree to give immortality by cutting into it and drinking the milk. The second story is of science where man tries to cure death by medicine. The third is by spirituality and by trying to reach xibalba in time to stop death. The point of all three is that death is a part of life and you can't stop it.

The tree is not the "tree of Izzy". It is the old growth tree from Guatemala which was discussed by the scientists. It is metaphorically a parallel to Izzy because he is trying to keep it alive just as he was originally trying to keep her alive.

( Besides, the seed pod he places over her grave has already released its seeds, though that could be a production oversight. )

It is all about meth, desire and appearance of life. three episode speaking about the focal point of our life. the story written by Izzi, shows some thing like religious opinion join to her believe about life, the hard working of tommy is like a symbolic presentation of people preoccupation in the life and forgetting about the way and thinking about destiny. there is a junction by Tomas story, a person that active to the real meaning of mortality by feel and experience of Izzi life.

In conclusion scene when Tommy kill the taboo about guardian of 'tree of life' joining of Tomm to the tree is like bringing the myth to the earth.