Much of the humour emanated from the 1960s and 1970s when Liverpool manager Bill Shankly mischievously sniped at the neighbours on the other side of Stanley Park at any opportunity.
"If Everton were playing at the bottom of the garden I'd pull the curtains," was one of Shankly's many putdowns.
So often Everton appeared to live life in the shadow of their neighbours, even the kudos of their crowning moment when they won the old first division title and the Cup Winners' Cup in 1985 being soured when English clubs were banned from Europe for five years following the Heysel disaster, meaning Everton's best team for a generation missed out on a tilt at the European Cup.
Well, whisper it quietly because the Premier League has a habit of making fools of anyone trying to predict its twists and turns, but Everton are back.
Back with a team full of youthful swagger in Ross Barkley, James McCarthy and Romelu Lukaku allied to the canny experience of Gareth Barry and Phil Jagielka.
Back with a manager in Roberto Martinez who could not play ugly football if he tried to and whose philosophy, with some irony, takes much from the old and simple yet devastatingly successful Liverpool philosophy of pass and move.
Back with a chance of finishing in the top four.
We will find out more on Sunday when Everton visit the Emirates Stadium and take on an Arsenal side who have set a blistering pace so far this season.
But, after beating Manchester United at Old Trafford for the first time in 21 years on Wednesday to make life even more difficult for former boss David Moyes, Everton lie fifth, one place on goal difference behind Liverpool and there is good reason to believe the way in which they have kicked on under Martinez is no fluke.
They have lost the fewest matches in the Premier League this season, their only defeat coming against Manchester City.
They possess the joint second meanest defence, having conceded 13 goals to Arsenal's 10. And they have beaten Chelsea, drawn with Liverpool and defeated United.
Wednesday's victory prompted Martinez to admit: "Today was more than a football match for us, it was trying to get over a mental block we have had for many, many years."
Even under the long and splendid reign of Moyes Everton could not beat United. They appeared cowed by English football's big boys, as if they did not really belong at the same table.
Not any more. And that is reason for all football fans to celebrate. Why? Because what is happening at Goodison Park is a throwback to good old-fashioned footballing principles.
No American, Russian, Far East or Middle East billionaire calling the shots from halfway across the world at Everton. Everton is run by chairman Bill Kenwright, a leading West End theatre producer and film producer who crucially was born in Liverpool and educated at the Liverpool Institute for Boys.
A wealthy man by ordinary standards but a pauper stacked up against the Sheikh Mansours, Roman Abramoviches and Stan Kroenkes of the football world.
He is a man who believes a football club should be run by a chairman pitting his faith and unstinting support in a hard-working and shrewd manager with an eye for talented players, who is left to get on with the job.
The work he and Martinez did in the close season in bringing Barry and Lukaku to Goodison on deadline day, albeit on loan, was masterly. Martinez, of course, had a solid foundation left by more than a decade of Moyes efficiency and parsimony. Yet the charismatic Spaniard has grasped that and moved the club on. Forget the jokes. It is time to take Everton seriously.
There was a time when unhappy footballers forfeited their share of any sell-on fee and did the decent thing by putting in a transfer request.
Now agents, such as Dimitar Berbatov's representative Emil Dantchev, skilfully circumvent such niceties. "I don't usually speculate as nobody knows what will happen in January but what I can tell you is he (Berbatov) is not happy at Fulham," Dantchev said this week.
"He would like, if possible, to find another option."
More's the pity, someone, somewhere, in the Premier League will almost certainly oblige.