Carbon cycle
In the diagram above, it demonstrates the carbon cycle. The carbon cycle is actually a big necessity in the taiga biome because of the large vegetation species. The Carbon cycle creates a steady amount of carbon available in the environment, helping plants when ever photosynthesis is being occurred. Without the Carbon cycle, plants wont be able to perform photosynthesis which is a big necessity for the environment and all of the different species living there who need oxygen to survive.
Water cycle
In the diagram above, it shows the typical water cycle. In the Taiga, Its water cycle is active. Since this biome has really unbalanced seasons, the water cycle helps it survive and also produce all the different species living on it.
Nitrogen Cycle
In the diagram above, it shows the Nitrogen cycle. The nitrogen cycle helps this biome actually convert all the non usable nitrates into usable ones that the plants can actually use themselves. If the nitrogen cycle wasn't available, over time all those nitrates would overflow causing effects to all the plants and animals living there.