Go back into time ;-)
Most Livorno (even the white) are ER/ER Ml/Ml s+/s+*s+/- I/I (because they must have yellow shanks and this is not possible on E/E, remember => Come "E" è responsabile anche della melanina epidermica presente nei tarsi è geneticamente impossibile avere un polli completamente neri basato sul Nero Esteso "E/E" (Australorp - Glu92Lys, Met71Thr) con tarsi gialli !)
So when you cross a White Livorno ER/ER Ml/Ml s+/s+ I/I to a Livorno gold neck e+/e+ s+/- (ml+/ml+ i+/i+)
you will become all progeny White => ER/e+ Ml/ml+ s+/s+*s+/- I/i+
When you cross now a young impure White rooster ER/e+ Ml/ml+ s+/s+ I/i+ with a gold neck hen e+/e+ s+/- (ml+/ml+ i+/i+)
you will become different phenotypes among several with a Dominant white gene in heterozygous :
ER/e+ Ml/ml+ s+/s+*s+/- I/i+ => White unicolor phenotype
ER/e+ ml+/ml+ s+/s+*s+/- I/i+ => Pile with too few red Betulla phenotype
e+/e+ Ml/ml+ s+/s+*s+/- I/i+ => Pile with too few red Quaglia phenotype
e+/e+ ml+/ml+ s+/s+*s+/- I/i+ => Pile with the correct phenotype