text (lettera, 10 + iTesto*15, 100);
As simple as that...

  if (fase == "introduzione") {
Beware, it can work in your sketch, but there are numerous cases where this kind of comparison will just fail.
See String in the Reference of Processing.

Some experiments w/ strings: 

All true:

---

String a = "abcdef";
String b = "abc" + "def";

final String c = "abc", d = "def";
//String c = "abc", d = "def";

String e = c + d;

println(a == b);
println(a == "abc" + "def");
println(a == c + "def");
println(a == e);

exit();

---

Last 1s false:

---

String a = "abcdef";
String b = "abc" + "def";

//final String c = "abc", d = "def";
String c = "abc", d = "def";

String e = c + d;

println(a == b);
println(a == "abc" + "def");
println(a == c + "def");
println(a == e);

exit();

---

Seems like concatenations using variables need final in all variables involved. 

I think that the lesson to be learned from GoToLoop's experiments is to avoid using == to compare the contents of Strings - as suggested by PhiLho have a look at the String of Processing.

You can also look at Java's API reference for String

To compare strings use the equals or equalsIgnoreCase methods e.g.

if (fase.equals("introduzione")) {

Oh I feel so dumb...I swear I tried hours to figure it out reading references and all! Thanks a lot to all for the comparison of strings, too, I'll be more accurate next time.

When the Java compiler sees literal strings "like this", if it finds twice the same string, it will intern it and reuse the reference for all of its occurrences.
So a == "foo" can work if there is a a = "foo" before.
If the variables are final, thus if they are constants, the compiler can still pre-compute the result of their concatenation, and still intern it. Same for "a" + "bc", probably false for "ABC".toLowerCase().
That's why it is safer to always use .equals(), if you don't want to guess when it will work and when it will not.

Thanks again! Yes, in my sketch "==" works but as soon as I can I will provide to optimize the comparison. I'm truly grateful for your fast and kind replies. :)