'The Rink': a musical saga of faded glitter;

''The Rink,'' the new musical at the Martin Beck Theatre, stars Chita Rivera and Liza Minnelli in a family-relations saga that can be both tough and sentimental as it tells what happens when prodigal daughter Angel (Miss Minnelli) returns home to the roller-skating rink her family once operated.

Angel arrives to discover that her mother Anna (Miss Rivera) has sold the onetime pleasure dome and that the wreckers are about to begin demolition. As co-inheritor, Angel vows to save the place. Playwright Terrence McNally, composer John Kander, and lyricist Fred Ebb take it from there.

Although the high-domed, steel-girdered rink designed by Peter Larkin is the show's most striking visual image, a more poignant metaphor is the glitter ball that begins twirling as Angel sings ''Colored Lights,'' the carrousel waltz that opens the show. A glitter ball is aspherical mirror that flecks the surrounding darkness with a thousand refractions - ''pink and yellow and green,'' in Angel's nostalgic recollection. A glitter ball without lights is like memory without magic or illusion.

It is the memory and the magic to which Angel clings and which she finds long since departed from the derelict rink Anna is now happily surrendering to the demolition gang. In their first duet, mother and daughter resume the wrangling that has gone on intermittently over the years - mostly by post card. The initial confrontation is interrupted for flashbacks dramatizing what led up to Angel's first leaving home.

There were Anna's hard-driving Italian in-laws, her ultimately faithless husband Dino (Scott Holmes). There were her years of prosperous but lonely survival as the proprietor of the rink. There was her insensitivity to the needs of the plain little Angel. And there was the deterioration of the Eastern Seaboard recreation park as it was taken over by punks and muggers.

The musical expression of the mother-daughter relationship and the events surrounding it cover an impressively wide range of mood and idiom. Kander and Ebb have written romantic numbers like ''Blue Crystal'' for Dino, ''We Can Make It'' for Anna, and ''Marry Me'' for Lenny (Jason Alexander as Anna's faithful admirer), plus the aformentioned ''Colored Lights.''

In ''What Happened to the Old Days,'' Anna and two elderly neighbors lament the passage of happier times and confront the brutal ugliness that has moved in. In ''After All These Years,'' and more particularly in the big roller-skating title number, the sextet of wreckers demonstrate their agile versatility.

In fact, versatility proves one of the particular pleasures of ''The Rink.'' The rink wreckers - performers Jason Alexander, Mel Johnson Jr., Scott Holmes, Scott Ellis, Frank Mastrocola, and Ronn Carroll - also play more than 20 other incidental characters, male and female.

Miss Rivera's Anna is a very tough and frequently foul-mouthed cookie. Mr. McNally has written her a flashy, hard-edged role and Miss Rivera acts it uncompromisingly, at the same time taking full advantage of the opportunities provided by the score and by Graciela Daniele's choreography. Miss Minnelli accomplishes the difficult acting task of portraying Angel at various ages of childhood and young womanhood. Besides her range of ages and emotions, Miss Minnelli, as the returning ex-hippie, helps bring the show to its surging emotional climax with ''All the Children in a Row.''

''The Rink'' looks back at the period culminating in the 1970s with a perspective touched by humor as well as sentimentality. The glitter ball sheds its colored lights as director A. J. Antoon guides the show through its smooth transitions from past to present and from song to dialogue. The show's principal problem may be that it has tried to cover too much ground. Except for its highlight numbers, the second act tends to pall.

Principal contributors to the superb production at the Martin Beck include Theoni V. Aldredge (costumes), Marc B. Weiss (lighting), and Michael Gibson (orchestrations). The splendid musical direction is by Paul Gemignani.