Python: intersection of nested lists where order matters

I would like to find the intersection between nested lists while maintaining the order.

taxa = [['E_pyrifoliae_Ep1_96', 'Bacteria', 'Proteobacteria', 'Gammaproteobacteria', 'Enterobacteriales', 'Enterobacteriaceae', 'Erwinia'],
 ['E_amylovora_CFBP1430', 'Bacteria', 'Proteobacteria', 'Gammaproteobacteria', 'Enterobacteriales', 'Enterobacteriaceae', 'Erwinia'], 
 ['E_amylovora_ATCC49946', 'Bacteria', 'Proteobacteria', 'Gammaproteobacteria', 'Enterobacteriales', 'Enterobacteriaceae', 'Erwinia']]

To find the intersection I have:

set.intersection(*map(set, taxa))

or

set(taxa[0]).intersection(*taxa)

but the original order is not kept.

set(['Erwinia', 'Gammaproteobacteria', 'Enterobacteriaceae', 'Enterobacteriales', 'Proteobacteria', 'Bacteria'])

Basically, what I need to do is find the last common element between the nested lists (they are taxanomic classifications ). So I don't need to find all the intersections, just the last one or all of them when I can just call on the last entry.

intersection_lst[-1]

In this instance I want the output to be 'Erwinia'.

Thanks for your help.