Today I checked which possibilities there are.
Flight by Alitalia from Catania to Venice: despite of five calls I couldn't get the information of whether and why (measures + packing) it is possible to transport the bicycle. One lady talked perfect English but passed me on. The next lady didn't talk any English so she passed me on. The third lady said I have to call another number. Then I talked to Roberta but the line broke down. Next it seemed she didn't hear me. This was the point I gave up.
Then I went to the railway station and asked the staff for a ticket to bologna with bike. He didn't speak English but his finger moved a no. I gave up again.
Now I have booked a ferry boat from Catania to Salerno.
So I'll leave Syracuse tomorrow for Catania. At 10 pm the boat will depart and will arrive next day at 11 pm at Salerno.
There I'll go to the railway station and hope to get a ticket for me and the bike ;-)
Otherwise I have to take the bike again ;-)