@CurlewKate I had to ask the internet as I thought it was PP but I couldn't say why. The internet says
Direct references in the text - "Do you remember how you used to play Pilgrim's Progress when you were little things? Nothing delighted you more than to... travel from the City of Destruction to the Celestial City."
Thematic Chapter Titles - Louisa May Alcott structured the entire first half of the novel around the plot of Bunyan's book. Many of the chapter titles are direct references to locations or characters from The Pilgrim's Progress
Chapter 6: "Beth Finds the Palace Beautiful"
Chapter 8: "Jo Meets Apollyon"
Chapter 9: "Meg Goes to Vanity Fair"
Chapter 13: "Castles in the Air" (referencing the Doubting Castle)
Epigraph, in LW he preface usually contains a poem adapted directly from John Bunyan. It begins: "Go then, my little Book, and show to all... That entertain, and bid thee welcome shall... may make them choose to be Pilgrims better, by far, than thee or me."
Why This Book?
The gift is a reference to a game the girls played as children called "Playing Pilgrims," where they would put "burdens" (bags of old clothes) on their backs and travel through their house from the "City of Destruction" (the cellar) to the "Celestial City" (the attic). Marmee gives them the books to remind them that, even though they are now older and facing the real hardships of the Civil War era, they can still find strength by treating life's difficulties as part of a meaningful journey.
I vividly remember that each book has its own colour tailored to each girl and I remember wanting that so badly for myself, to reach under my pillow and find a book. We used the local library as we were poor so bought books were a luxury item.