Branch Out - Monkey Edition

Question

The Monkey has swung home to find his tree all in pieces.

He likes order and scoops up all his 'tree-parts' and sets them out in 3 groups.

The Monkey's 3 nested lists:

STEP = [['S', '1', 'B', '3'], ['S', '3', 'B', '11'], ['S', '5', 'B', '12'], ['S', '4', 'B', '13'], ['S', '2', 'B', '14']]

TRANSITION = [['T', '2', 'B', '4'], ['T', '7', 'B', '4'], ['T', '3', 'S', '4'], ['T', '5', 'S', '5'], ['T', '1', 'S', '2'], ['T', '8', 'S', '2'], ['T', '6', 'S', '1'], ['T', '9', 'S', '2'], ['T', '4', 'S', '1'], ['T', '10', 'S', '1']]

BRANCH = [['B', '3', 'T', '1'], ['B', '3', 'T', '7'], ['B', '4', 'S', '3'], ['B', '11', 'T', '3'], ['B', '11', 'T', '5'], ['B', '12', 'T', '6'], ['B', '12', 'T', '8'], ['B', '13', 'T', '4'], ['B', '13', 'T', '9'], ['B', '14', 'T', '2'], ['B', '14', 'T', '10']]

Each element holds information as such:

# Example

STEP[0]  =  ['S', '1', 'B', '3']

Where:

• 'S' is the STEP type
• '1' is the STEP number id
• 'B' is the linked BRANCH type
• '3' is the linked BRANCH number id

Starting from a STEP the data is all linked, so using the linked reference you can find the next element and the next until another STEP is reached.

This is some parameters of the data:

• STEPS are connected to single BRANCHES
• BRANCHES are connected to one or more TRANSITIONS
• TRANSITIONS can be connected to a single BRANCH or STEP

The BRANCH data can have a fork where a single BRANCH id has one or more options for TRANSITIONS.

Re-create this monkey's tree (nested list format is fine) in the shortest way possible (he is not a fan of long instructions):

           [S1]
            |          
          B3|_________ 
            |         |
           [T1]     [T7]
            |         |
            |       B4|
            |         |
           [S2]     [S3]

And list all the routes on this tree:

Routes = [[S1, B3, T1, S2], [S1, B3, T7, B4, S3]]

UPDATE: This is Code-golf and from the data given you need to output the display of the tree ( This can be different from my example but requires the same elements to be displayed in any format) and as you cycle through the problem to output all the possible routes as a BONUS.